Details

analyze449.0ms (0.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample36.0ms (0%)

Algorithm

1×

intervals

Results

9.0ms	179×	body	128	valid
8.0ms	32×	body	2048	valid
4.0ms	24×	body	1024	valid
2.0ms	7×	body	4096	valid
2.0ms	11×	body	512	valid
1.0ms	17×	body	128	invalid
1.0ms	12×	body	128	nan
0.0ms	3×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify438.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (340.0ms)

Iter	Nodes	Cost
0	1834	24
1	1834	24

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

30.6b

Counts

2 → 2

Compiler

Compiled 16 to 13 computations (18.8% saved)

localize12.0ms (0%)

Local error

Found 8 expressions with local error:

0.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.8b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
0.1b	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
0.0b	(.f64 4 (.f64 a c))
0.1b	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
0.8b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
0.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
20.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite39.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64_1123`
21×	`*-un-lft-identity_binary64_1101`
10×	`add-log-exp_binary64_1140`
9×	`add-exp-log_binary64_1139` `sqrt-prod_binary64_1117` `add-cube-cbrt_binary64_1136` `add-cbrt-cube_binary64_1137`
7×	`associate-/l*_binary64_1046` `times-frac_binary64_1107` `cancel-sign-sub-inv_binary64_1067`
6×	`difference-of-squares_binary64_1070` `distribute-lft-out--_binary64_1053`
5×	`pow1_binary64_1162`
4×	`flip--_binary64_1076` `flip3--_binary64_1105`
3×	`distribute-rgt-neg-in_binary64_1059` `diff-log_binary64_1193`
2×	`sub-neg_binary64_1094` `associate-/l/_binary64_1048` `sqrt-div_binary64_1118` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135`
1×	`rem-sqrt-square_binary64_1114` `cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `frac-2neg_binary64_1112` `sqrt-pow1_binary64_1119` `neg-log_binary64_1194` `clear-num_binary64_1100` `neg-sub0_binary64_1096` `div-inv_binary64_1098` `associate-/r*_binary64_1045` `associate--l-_binary64_1039` `pow1/2_binary64_1181` `div-sub_binary64_1106`

Counts

4 → 82

Calls

8 calls:

13.0ms	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
9.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.0ms	(.f64 4 (.f64 a c))

series734.0ms (0.6%)

Counts

4 → 77

Calls

4 calls:

241.0ms	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
183.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
155.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
154.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

Compiler

Compiled 2337 to 1975 computations (15.5% saved)

simplify85.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4920	3383
1	4920	3383

localize11.0ms (0%)

Local error

Found 8 expressions with local error:

0.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.8b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
0.1b	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
0.0b	(.f64 4 (.f64 a c))
0.1b	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
0.8b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
0.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
20.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite30.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64_1101`
15×	`add-sqr-sqrt_binary64_1123`
14×	`add-cube-cbrt_binary64_1136`
12×	`times-frac_binary64_1107`
8×	`add-log-exp_binary64_1140`
6×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
5×	`distribute-lft-out_binary64_1052` `pow1_binary64_1162`
4×	`associate-/l*_binary64_1046`
3×	`sqrt-prod_binary64_1117` `associate-/r*_binary64_1045`
2×	`flip--_binary64_1076` `flip3--_binary64_1105` `flip3-+_binary64_1104` `associate-/l/_binary64_1048` `sqrt-div_binary64_1118` `flip-+_binary64_1075`
1×	`diff-log_binary64_1193` `rem-sqrt-square_binary64_1114` `frac-2neg_binary64_1112` `sum-log_binary64_1192` `sub-neg_binary64_1094` `sqrt-pow1_binary64_1119` `clear-num_binary64_1100` `div-inv_binary64_1098` `+-commutative_binary64_1031` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `cancel-sign-sub-inv_binary64_1067` `pow1/2_binary64_1181`

Counts

4 → 72

Calls

8 calls:

8.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
0.0ms	(.f64 4 (.f64 a c))

series703.0ms (0.5%)

Counts

4 → 77

Calls

4 calls:

217.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
184.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
156.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
146.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

Compiler

Compiled 2316 to 1954 computations (15.6% saved)

simplify86.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4963	3079
1	4963	3079

prune1.8s (1.4%)

Pruning

125 alts after pruning (123 fresh and 2 done)

	Pruned	Kept	Total
New	185	123	308
Fresh	0	0	0
Picked	0	0	0
Done	0	2	2
Total	185	125	310

Error

5.7b

Counts

310 → 125

Compiler

Compiled 7375 to 4473 computations (39.3% saved)

localize18.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
0.1b	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))))) (.f64 2 a))
0.0b	(.f64 4 (.f64 a c))
0.0b	(.f64 4 (.f64 a c))
0.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
20.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
20.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
20.7b	(sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))

rewrite34.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`sqrt-pow1_binary64_1119` `sqrt-div_binary64_1118`
22×	`pow1_binary64_1162`
11×	`pow1/2_binary64_1181`
9×	`flip--_binary64_1076` `flip3--_binary64_1105`
8×	`add-sqr-sqrt_binary64_1123`
7×	`sqrt-prod_binary64_1117`
6×	`*-un-lft-identity_binary64_1101` `add-log-exp_binary64_1140` `add-cube-cbrt_binary64_1136`
5×	`pow-prod-up_binary64_1171`
4×	`frac-times_binary64_1111` `add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
3×	`rem-sqrt-square_binary64_1114` `pow-sqr_binary64_1074` `pow-prod-down_binary64_1172`
2×	`associate-r/_binary64_1043` `associate-l/_binary64_1044`
1×	`pow-plus_binary64_1164` `diff-log_binary64_1193` `sub-neg_binary64_1094` `cancel-sign-sub-inv_binary64_1067` `pow2_binary64_1182`

Counts

4 → 74

Calls

8 calls:

12.0ms	(sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
0.0ms	(.f64 4 (.f64 a c))

series659.0ms (0.5%)

Counts

4 → 75

Calls

4 calls:

169.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
167.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
161.0ms	(sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
161.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

Compiler

Compiled 3487 to 2687 computations (22.9% saved)

simplify99.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4936	2595
1	4936	2595

localize4.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

localize17.0ms (0%)

Local error

Found 8 expressions with local error:

0.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.8b	(-.f64 (neg.f64 b) (.f64 1 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))))
0.1b	(/.f64 (-.f64 (neg.f64 b) (.f64 1 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (*.f64 2 a))
0.0b	(.f64 4 (.f64 a c))
0.1b	(/.f64 (-.f64 (neg.f64 b) (.f64 1 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (*.f64 2 a))
0.8b	(-.f64 (neg.f64 b) (.f64 1 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))))
0.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
20.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite28.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64_1101`
10×	`add-log-exp_binary64_1140`
9×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
8×	`add-sqr-sqrt_binary64_1123`
7×	`add-cube-cbrt_binary64_1136`
6×	`distribute-lft-out--_binary64_1053`
5×	`pow1_binary64_1162` `associate-/l*_binary64_1046` `times-frac_binary64_1107`
4×	`flip--_binary64_1076` `flip3--_binary64_1105`
3×	`distribute-rgt-neg-in_binary64_1059` `diff-log_binary64_1193` `sqrt-prod_binary64_1117`
2×	`sub-neg_binary64_1094` `associate-/l/_binary64_1048` `sqrt-div_binary64_1118` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `cancel-sign-sub-inv_binary64_1067`
1×	`rem-sqrt-square_binary64_1114` `cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `frac-2neg_binary64_1112` `sqrt-pow1_binary64_1119` `neg-log_binary64_1194` `clear-num_binary64_1100` `neg-sub0_binary64_1096` `div-inv_binary64_1098` `associate-/r*_binary64_1045` `associate--l-_binary64_1039` `pow1/2_binary64_1181` `div-sub_binary64_1106`

Counts

4 → 71

Calls

8 calls:

8.0ms	(/.f64 (-.f64 (neg.f64 b) (.f64 1 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (*.f64 2 a))
5.0ms	(-.f64 (neg.f64 b) (.f64 1 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.0ms	(.f64 4 (.f64 a c))

series762.0ms (0.6%)

Counts

4 → 77

Calls

4 calls:

248.0ms	(/.f64 (-.f64 (neg.f64 b) (.f64 1 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (*.f64 2 a))
199.0ms	(-.f64 (neg.f64 b) (.f64 1 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))))
158.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
157.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 2447 to 2085 computations (14.8% saved)

simplify99.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4958	3013
1	4958	3013

localize14.0ms (0%)

Local error

Found 8 expressions with local error:

0.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.8b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
0.1b	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 a 2))
0.0b	(.f64 4 (.f64 a c))
0.8b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
0.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
2.0b	(exp.f64 (log.f64 (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 a 2))))
20.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite42.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64_1123`
18×	`*-un-lft-identity_binary64_1101`
11×	`exp-sum_binary64_1147` `log-prod_binary64_1187`
10×	`add-log-exp_binary64_1140` `add-cube-cbrt_binary64_1136`
8×	`sqrt-prod_binary64_1117`
7×	`times-frac_binary64_1107` `cancel-sign-sub-inv_binary64_1067`
6×	`pow1_binary64_1162`
4×	`difference-of-squares_binary64_1070` `add-exp-log_binary64_1139` `distribute-lft-out--_binary64_1053` `exp-prod_binary64_1153` `add-cbrt-cube_binary64_1137`
3×	`diff-log_binary64_1193` `flip--_binary64_1076` `flip3--_binary64_1105`
2×	`distribute-rgt-neg-in_binary64_1059` `sub-neg_binary64_1094` `sqrt-div_binary64_1118`
1×	`rem-sqrt-square_binary64_1114` `rem-exp-log_binary64_1141` `sqrt-pow1_binary64_1119` `exp-diff_binary64_1149` `neg-log_binary64_1194` `neg-sub0_binary64_1096` `div-inv_binary64_1098` `log-pow_binary64_1190` `log-div_binary64_1188` `associate--l-_binary64_1039` `pow1/2_binary64_1181`

Counts

4 → 74

Calls

8 calls:

15.0ms	(exp.f64 (log.f64 (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 a 2))))
10.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
0.0ms	(.f64 4 (.f64 a c))

series743.0ms (0.6%)

Counts

4 → 58

Calls

4 calls:

329.0ms	(exp.f64 (log.f64 (/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 a 2))))
157.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
140.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
117.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 2314 to 1929 computations (16.6% saved)

simplify60.0ms (0%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5224	2798

localize15.0ms (0%)

Local error

Found 8 expressions with local error:

0.8b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
0.0b	(.f64 4 (.f64 a c))
0.0b	(.f64 4 (.f64 a c))
0.0b	(/.f64 (sqrt.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (/.f64 a (/.f64 (sqrt.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) 2)))
0.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
20.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
20.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite24.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64_1123` `add-log-exp_binary64_1140`
6×	`*-un-lft-identity_binary64_1101` `pow1_binary64_1162` `sqrt-prod_binary64_1117` `add-cube-cbrt_binary64_1136`
4×	`add-exp-log_binary64_1139` `flip--_binary64_1076` `flip3--_binary64_1105` `add-cbrt-cube_binary64_1137` `sqrt-div_binary64_1118`
2×	`diff-log_binary64_1193` `rem-sqrt-square_binary64_1114` `sub-neg_binary64_1094` `sqrt-pow1_binary64_1119` `cancel-sign-sub-inv_binary64_1067` `pow1/2_binary64_1181`

Counts

4 → 54

Calls

8 calls:

4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
0.0ms	(/.f64 (sqrt.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (/.f64 a (/.f64 (sqrt.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) 2)))

series528.0ms (0.4%)

Counts

4 → 58

Calls

4 calls:

171.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
167.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
96.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
93.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 3066 to 2244 computations (26.8% saved)

simplify72.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4919	1560
1	4919	1560

prune7.5s (5.8%)

Pruning

257 alts after pruning (250 fresh and 7 done)

	Pruned	Kept	Total
New	404	137	541
Fresh	5	113	118
Picked	0	0	0
Done	0	7	7
Total	409	257	666

Error

5.7b

Counts

666 → 257

Compiler

Compiled 16090 to 9907 computations (38.4% saved)

localize15.0ms (0%)

Local error

Found 8 expressions with local error:

0.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.8b	(-.f64 (neg.f64 b) (.f64 1 (fabs.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))))
0.1b	(/.f64 (-.f64 (neg.f64 b) (.f64 1 (fabs.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))))) (*.f64 2 a))
0.0b	(.f64 4 (.f64 a c))
0.1b	(/.f64 (-.f64 (neg.f64 b) (.f64 1 (fabs.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))))) (*.f64 2 a))
0.8b	(-.f64 (neg.f64 b) (.f64 1 (fabs.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))))
0.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
20.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite28.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64_1101`
10×	`add-log-exp_binary64_1140`
9×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
8×	`add-sqr-sqrt_binary64_1123`
7×	`add-cube-cbrt_binary64_1136`
6×	`distribute-lft-out--_binary64_1053`
5×	`pow1_binary64_1162` `associate-/l*_binary64_1046` `times-frac_binary64_1107`
4×	`flip--_binary64_1076` `flip3--_binary64_1105`
3×	`distribute-rgt-neg-in_binary64_1059` `diff-log_binary64_1193` `sqrt-prod_binary64_1117`
2×	`sub-neg_binary64_1094` `associate-/l/_binary64_1048` `sqrt-div_binary64_1118` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `cancel-sign-sub-inv_binary64_1067`
1×	`rem-sqrt-square_binary64_1114` `cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `frac-2neg_binary64_1112` `sqrt-pow1_binary64_1119` `neg-log_binary64_1194` `clear-num_binary64_1100` `neg-sub0_binary64_1096` `div-inv_binary64_1098` `associate-/r*_binary64_1045` `associate--l-_binary64_1039` `pow1/2_binary64_1181` `div-sub_binary64_1106`

Counts

4 → 71

Calls

8 calls:

7.0ms	(/.f64 (-.f64 (neg.f64 b) (.f64 1 (fabs.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))))) (*.f64 2 a))
5.0ms	(-.f64 (neg.f64 b) (.f64 1 (fabs.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))))
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
0.0ms	(.f64 4 (.f64 a c))

series637.0ms (0.5%)

Counts

4 → 61

Calls

4 calls:

211.0ms	(/.f64 (-.f64 (neg.f64 b) (.f64 1 (fabs.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))))) (*.f64 2 a))
180.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
155.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
90.0ms	(-.f64 (neg.f64 b) (.f64 1 (fabs.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))))

Compiler

Compiled 2016 to 1775 computations (12% saved)

simplify74.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	6750	2670

localize3.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify9.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

localize15.0ms (0%)

Local error

Found 8 expressions with local error:

4.5b	(/.f64 (.f64 b b) (sqrt.f64 (.f64 a (*.f64 c -4))))
2.3b	(/.f64 (-.f64 (neg.f64 b) (+.f64 (sqrt.f64 (.f64 a (.f64 c -4))) (.f64 1/2 (/.f64 (.f64 b b) (sqrt.f64 (.f64 a (.f64 c -4))))))) (*.f64 2 a))
0.0b	(-.f64 (neg.f64 b) (+.f64 (sqrt.f64 (.f64 a (.f64 c -4))) (.f64 1/2 (/.f64 (.f64 b b) (sqrt.f64 (.f64 a (.f64 c -4)))))))
0.0b	(.f64 1/2 (/.f64 (.f64 b b) (sqrt.f64 (.f64 a (.f64 c -4)))))
2.3b	(/.f64 (-.f64 (neg.f64 b) (+.f64 (sqrt.f64 (.f64 a (.f64 c -4))) (.f64 1/2 (/.f64 (.f64 b b) (sqrt.f64 (.f64 a (.f64 c -4))))))) (*.f64 2 a))
4.5b	(/.f64 (.f64 b b) (sqrt.f64 (.f64 a (*.f64 c -4))))
13.4b	(sqrt.f64 (.f64 a (.f64 c -4)))
13.4b	(sqrt.f64 (.f64 a (.f64 c -4)))

rewrite39.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`*-un-lft-identity_binary64_1101` `pow1_binary64_1162`
14×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
12×	`add-sqr-sqrt_binary64_1123`
10×	`times-frac_binary64_1107`
8×	`add-cube-cbrt_binary64_1136`
7×	`associate-/l*_binary64_1046`
6×	`sqrt-pow1_binary64_1119` `pow-prod-down_binary64_1172`
5×	`associate-/r*_binary64_1045`
4×	`add-log-exp_binary64_1140` `distribute-lft-out--_binary64_1053` `sqrt-prod_binary64_1117` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135`
2×	`distribute-rgt-neg-in_binary64_1059` `cbrt-unprod_binary64_1134` `difference-of-squares_binary64_1070` `prod-exp_binary64_1150` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/l/_binary64_1048` `div-inv_binary64_1098` `pow1/2_binary64_1181`
1×	`flip--_binary64_1076` `flip3--_binary64_1105` `div-sub_binary64_1106`

Counts

4 → 77

Calls

8 calls:

14.0ms	(/.f64 (-.f64 (neg.f64 b) (+.f64 (sqrt.f64 (.f64 a (.f64 c -4))) (.f64 1/2 (/.f64 (.f64 b b) (sqrt.f64 (.f64 a (.f64 c -4))))))) (*.f64 2 a))
9.0ms	(/.f64 (.f64 b b) (sqrt.f64 (.f64 a (*.f64 c -4))))
4.0ms	(sqrt.f64 (.f64 a (.f64 c -4)))
4.0ms	(sqrt.f64 (.f64 a (.f64 c -4)))
0.0ms	(.f64 1/2 (/.f64 (.f64 b b) (sqrt.f64 (.f64 a (.f64 c -4)))))

series607.0ms (0.5%)

Counts

4 → 36

Calls

4 calls:

382.0ms	(/.f64 (-.f64 (neg.f64 b) (+.f64 (sqrt.f64 (.f64 a (.f64 c -4))) (.f64 1/2 (/.f64 (.f64 b b) (sqrt.f64 (.f64 a (.f64 c -4))))))) (*.f64 2 a))
143.0ms	(/.f64 (.f64 b b) (sqrt.f64 (.f64 a (*.f64 c -4))))
42.0ms	(sqrt.f64 (.f64 a (.f64 c -4)))
40.0ms	(sqrt.f64 (.f64 a (.f64 c -4)))

Compiler

Compiled 1837 to 1506 computations (18% saved)

simplify88.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4976	2606
1	4976	2606

localize23.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (*.f64 a 2))
0.0b	(.f64 4 (.f64 a c))
0.0b	(.f64 4 (.f64 a c))
0.0b	(.f64 4 (.f64 a c))
17.2b	(-.f64 (.f64 (neg.f64 b) (neg.f64 b)) (.f64 (.f64 1 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 1 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))))
20.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
20.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
20.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite28.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_1123`
9×	`sqrt-prod_binary64_1117`
7×	`*-un-lft-identity_binary64_1101` `pow1_binary64_1162` `add-cube-cbrt_binary64_1136`
6×	`add-log-exp_binary64_1140` `sqrt-div_binary64_1118`
4×	`add-exp-log_binary64_1139` `flip--_binary64_1076` `flip3--_binary64_1105` `add-cbrt-cube_binary64_1137`
3×	`rem-sqrt-square_binary64_1114` `sqrt-pow1_binary64_1119` `pow1/2_binary64_1181`
1×	`diff-log_binary64_1193` `difference-of-squares_binary64_1070` `sub-neg_binary64_1094` `cancel-sign-sub-inv_binary64_1067`

Counts

4 → 58

Calls

8 calls:

6.0ms	(-.f64 (.f64 (neg.f64 b) (neg.f64 b)) (.f64 (.f64 1 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 1 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
0.0ms	(.f64 4 (.f64 a c))

series641.0ms (0.5%)

Counts

4 → 69

Calls

4 calls:

185.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
179.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
176.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
100.0ms	(-.f64 (.f64 (neg.f64 b) (neg.f64 b)) (.f64 (.f64 1 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 1 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))))

Compiler

Compiled 5076 to 3456 computations (31.9% saved)

simplify67.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5280	2257

localize29.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(/.f64 (-.f64 (neg.f64 b) (/.f64 (sqrt.f64 (-.f64 (pow.f64 b 6) (pow.f64 (.f64 4 (.f64 a c)) 3))) (sqrt.f64 (+.f64 (pow.f64 b 4) (.f64 4 (.f64 (.f64 a c) (+.f64 (.f64 b b) (.f64 4 (.f64 a c))))))))) (*.f64 2 a))
0.0b	(.f64 4 (.f64 a c))
0.0b	(.f64 4 (.f64 a c))
0.0b	(.f64 4 (.f64 (.f64 a c) (+.f64 (.f64 b b) (.f64 4 (.f64 a c)))))
7.2b	(+.f64 (pow.f64 b 4) (.f64 4 (.f64 (.f64 a c) (+.f64 (.f64 b b) (.f64 4 (.f64 a c))))))
13.9b	(sqrt.f64 (-.f64 (pow.f64 b 6) (pow.f64 (.f64 4 (.f64 a c)) 3)))
16.9b	(sqrt.f64 (+.f64 (pow.f64 b 4) (.f64 4 (.f64 (.f64 a c) (+.f64 (.f64 b b) (.f64 4 (.f64 a c)))))))
31.4b	(/.f64 (sqrt.f64 (-.f64 (pow.f64 b 6) (pow.f64 (.f64 4 (.f64 a c)) 3))) (sqrt.f64 (+.f64 (pow.f64 b 4) (.f64 4 (.f64 (.f64 a c) (+.f64 (.f64 b b) (.f64 4 (.f64 a c))))))))

rewrite76.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

125×	`sqrt-prod_binary64_1117`
106×	`add-sqr-sqrt_binary64_1123`
78×	`times-frac_binary64_1107`
64×	`*-un-lft-identity_binary64_1101`
48×	`difference-of-squares_binary64_1070` `add-cube-cbrt_binary64_1136`
40×	`sqr-pow_binary64_1073`
16×	`unpow-prod-down_binary64_1180`
13×	`associate-/l*_binary64_1046`
8×	`distribute-lft-out--_binary64_1053` `sqrt-div_binary64_1118`
6×	`add-log-exp_binary64_1140` `add-exp-log_binary64_1139` `pow1_binary64_1162` `add-cbrt-cube_binary64_1137` `associate-/r*_binary64_1045`
4×	`distribute-lft-in_binary64_1050` `associate-+r+_binary64_1033` `distribute-rgt-in_binary64_1051`
3×	`flip3-+_binary64_1104` `flip-+_binary64_1075`
2×	`rem-sqrt-square_binary64_1114` `sqrt-pow1_binary64_1119` `flip--_binary64_1076` `flip3--_binary64_1105` `associate-/l/_binary64_1048` `associate-/r/_binary64_1047` `pow1/2_binary64_1181`
1×	`sqrt-undiv_binary64_1122` `frac-2neg_binary64_1112` `sum-log_binary64_1192` `clear-num_binary64_1100` `div-inv_binary64_1098` `+-commutative_binary64_1031` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135`

Counts

4 → 166

Calls

8 calls:

17.0ms	(/.f64 (sqrt.f64 (-.f64 (pow.f64 b 6) (pow.f64 (.f64 4 (.f64 a c)) 3))) (sqrt.f64 (+.f64 (pow.f64 b 4) (.f64 4 (.f64 (.f64 a c) (+.f64 (.f64 b b) (.f64 4 (.f64 a c))))))))
8.0ms	(sqrt.f64 (-.f64 (pow.f64 b 6) (pow.f64 (.f64 4 (.f64 a c)) 3)))
6.0ms	(+.f64 (pow.f64 b 4) (.f64 4 (.f64 (.f64 a c) (+.f64 (.f64 b b) (.f64 4 (.f64 a c))))))
5.0ms	(sqrt.f64 (+.f64 (pow.f64 b 4) (.f64 4 (.f64 (.f64 a c) (+.f64 (.f64 b b) (.f64 4 (.f64 a c)))))))
0.0ms	(.f64 4 (.f64 (.f64 a c) (+.f64 (.f64 b b) (.f64 4 (.f64 a c)))))

series1.3s (1%)

Counts

4 → 83

Calls

4 calls:

515.0ms	(+.f64 (pow.f64 b 4) (.f64 4 (.f64 (.f64 a c) (+.f64 (.f64 b b) (.f64 4 (.f64 a c))))))
299.0ms	(/.f64 (sqrt.f64 (-.f64 (pow.f64 b 6) (pow.f64 (.f64 4 (.f64 a c)) 3))) (sqrt.f64 (+.f64 (pow.f64 b 4) (.f64 4 (.f64 (.f64 a c) (+.f64 (.f64 b b) (.f64 4 (.f64 a c))))))))
261.0ms	(sqrt.f64 (+.f64 (pow.f64 b 4) (.f64 4 (.f64 (.f64 a c) (+.f64 (.f64 b b) (.f64 4 (.f64 a c)))))))
199.0ms	(sqrt.f64 (-.f64 (pow.f64 b 6) (pow.f64 (.f64 4 (.f64 a c)) 3)))

Compiler

Compiled 4205 to 3365 computations (20% saved)

simplify147.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

249 → 249

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5053	12657

prune16.0s (12.5%)

Pruning

464 alts after pruning (453 fresh and 11 done)

	Pruned	Kept	Total
New	400	221	621
Fresh	13	232	245
Picked	0	0	0
Done	1	11	12
Total	414	464	878

Error

3.3b

Counts

878 → 464

Compiler

Compiled 32562 to 20885 computations (35.9% saved)

localize12.0ms (0%)

Local error

Found 8 expressions with local error:

0.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.8b	(+.f64 b (fabs.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
0.1b	(/.f64 (+.f64 b (fabs.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
0.0b	(.f64 4 (.f64 a c))
0.1b	(/.f64 (+.f64 b (fabs.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
0.8b	(+.f64 b (fabs.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
0.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
20.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite25.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64_1101`
15×	`add-sqr-sqrt_binary64_1123`
14×	`add-cube-cbrt_binary64_1136`
12×	`times-frac_binary64_1107`
8×	`add-log-exp_binary64_1140`
6×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
5×	`distribute-lft-out_binary64_1052` `pow1_binary64_1162`
4×	`associate-/l*_binary64_1046`
3×	`sqrt-prod_binary64_1117` `associate-/r*_binary64_1045`
2×	`flip--_binary64_1076` `flip3--_binary64_1105` `flip3-+_binary64_1104` `associate-/l/_binary64_1048` `sqrt-div_binary64_1118` `flip-+_binary64_1075`
1×	`diff-log_binary64_1193` `rem-sqrt-square_binary64_1114` `frac-2neg_binary64_1112` `sum-log_binary64_1192` `sub-neg_binary64_1094` `sqrt-pow1_binary64_1119` `clear-num_binary64_1100` `div-inv_binary64_1098` `+-commutative_binary64_1031` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `cancel-sign-sub-inv_binary64_1067` `pow1/2_binary64_1181`

Counts

4 → 72

Calls

8 calls:

6.0ms	(/.f64 (+.f64 b (fabs.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
3.0ms	(+.f64 b (fabs.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
0.0ms	(.f64 4 (.f64 a c))

series536.0ms (0.4%)

Counts

4 → 61

Calls

4 calls:

160.0ms	(/.f64 (+.f64 b (fabs.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
153.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
150.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
73.0ms	(+.f64 b (fabs.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))

Compiler

Compiled 1781 to 1540 computations (13.5% saved)

simplify96.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4967	2716
1	4967	2716

localize4.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

localize15.0ms (0%)

Local error

Found 8 expressions with local error:

0.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.8b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
0.0b	(exp.f64 (log.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))
0.0b	(.f64 4 (.f64 a c))
0.0b	(exp.f64 (log.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))
0.8b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
0.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
20.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite42.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64_1123`
17×	`*-un-lft-identity_binary64_1101`
10×	`add-log-exp_binary64_1140`
9×	`add-cube-cbrt_binary64_1136`
8×	`sqrt-prod_binary64_1117`
7×	`exp-sum_binary64_1147` `log-prod_binary64_1187` `cancel-sign-sub-inv_binary64_1067`
6×	`pow1_binary64_1162`
4×	`difference-of-squares_binary64_1070` `add-exp-log_binary64_1139` `distribute-lft-out--_binary64_1053` `flip--_binary64_1076` `exp-prod_binary64_1153` `flip3--_binary64_1105` `add-cbrt-cube_binary64_1137`
3×	`diff-log_binary64_1193`
2×	`distribute-rgt-neg-in_binary64_1059` `sub-neg_binary64_1094` `exp-diff_binary64_1149` `sqrt-div_binary64_1118` `log-div_binary64_1188`
1×	`rem-sqrt-square_binary64_1114` `rem-exp-log_binary64_1141` `sqrt-pow1_binary64_1119` `neg-log_binary64_1194` `neg-sub0_binary64_1096` `log-pow_binary64_1190` `associate--l-_binary64_1039` `pow1/2_binary64_1181`

Counts

4 → 71

Calls

8 calls:

10.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
10.0ms	(exp.f64 (log.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))
6.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.0ms	(.f64 4 (.f64 a c))

series575.0ms (0.4%)

Counts

4 → 52

Calls

4 calls:

211.0ms	(exp.f64 (log.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))
161.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
118.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
85.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 1977 to 1633 computations (17.4% saved)

simplify90.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4925	2290
1	4925	2290

localize27.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(/.f64 (+.f64 b (sqrt.f64 (/.f64 (-.f64 (pow.f64 b 6) (pow.f64 (.f64 4 (.f64 a c)) 3)) (+.f64 (pow.f64 b 4) (.f64 4 (.f64 (.f64 a c) (+.f64 (.f64 b b) (.f64 4 (.f64 a c))))))))) a)
0.0b	(.f64 4 (.f64 a c))
0.0b	(.f64 4 (.f64 a c))
0.0b	(.f64 4 (.f64 (.f64 a c) (+.f64 (.f64 b b) (.f64 4 (.f64 a c)))))
3.0b	(.f64 (.f64 a c) (+.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
7.2b	(+.f64 (pow.f64 b 4) (.f64 4 (.f64 (.f64 a c) (+.f64 (.f64 b b) (.f64 4 (.f64 a c))))))
20.7b	(sqrt.f64 (/.f64 (-.f64 (pow.f64 b 6) (pow.f64 (.f64 4 (.f64 a c)) 3)) (+.f64 (pow.f64 b 4) (.f64 4 (.f64 (.f64 a c) (+.f64 (.f64 b b) (.f64 4 (.f64 a c))))))))
42.7b	(/.f64 (-.f64 (pow.f64 b 6) (pow.f64 (.f64 4 (.f64 a c)) 3)) (+.f64 (pow.f64 b 4) (.f64 4 (.f64 (.f64 a c) (+.f64 (.f64 b b) (.f64 4 (.f64 a c)))))))

rewrite80.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

86×	`add-sqr-sqrt_binary64_1123`
61×	`times-frac_binary64_1107`
48×	`*-un-lft-identity_binary64_1101`
42×	`difference-of-squares_binary64_1070`
36×	`sqrt-prod_binary64_1117`
35×	`sqr-pow_binary64_1073`
34×	`add-cube-cbrt_binary64_1136`
14×	`unpow-prod-down_binary64_1180`
11×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
10×	`pow1_binary64_1162` `associate-/l*_binary64_1046`
7×	`distribute-lft-out--_binary64_1053`
6×	`add-log-exp_binary64_1140`
5×	`distribute-lft-in_binary64_1050` `distribute-rgt-in_binary64_1051`
4×	`associate-+r+_binary64_1033` `flip3-+_binary64_1104` `associate-/r/_binary64_1047` `flip-+_binary64_1075`
3×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `associate-r_binary64_1041` `pow-prod-down_binary64_1172` `associate-/r*_binary64_1045`
2×	`rem-sqrt-square_binary64_1114` `associate-/l/_binary64_1048` `associate-*r/_binary64_1043` `div-inv_binary64_1098`
1×	`-commutative_binary64_1032` `frac-2neg_binary64_1112` `sum-log_binary64_1192` `sqrt-pow1_binary64_1119` `clear-num_binary64_1100` `flip--_binary64_1076` `flip3--_binary64_1105` `+-commutative_binary64_1031` `sqrt-div_binary64_1118` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `associate-l*_binary64_1042` `pow1/2_binary64_1181` `div-sub_binary64_1106`

Counts

4 → 145

Calls

8 calls:

16.0ms	(/.f64 (-.f64 (pow.f64 b 6) (pow.f64 (.f64 4 (.f64 a c)) 3)) (+.f64 (pow.f64 b 4) (.f64 4 (.f64 (.f64 a c) (+.f64 (.f64 b b) (.f64 4 (.f64 a c)))))))
15.0ms	(sqrt.f64 (/.f64 (-.f64 (pow.f64 b 6) (pow.f64 (.f64 4 (.f64 a c)) 3)) (+.f64 (pow.f64 b 4) (.f64 4 (.f64 (.f64 a c) (+.f64 (.f64 b b) (.f64 4 (.f64 a c))))))))
9.0ms	(.f64 (.f64 a c) (+.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
6.0ms	(+.f64 (pow.f64 b 4) (.f64 4 (.f64 (.f64 a c) (+.f64 (.f64 b b) (.f64 4 (.f64 a c))))))
0.0ms	(.f64 4 (.f64 (.f64 a c) (+.f64 (.f64 b b) (.f64 4 (.f64 a c)))))

series1.8s (1.4%)

Counts

4 → 82

Calls

4 calls:

701.0ms	(/.f64 (-.f64 (pow.f64 b 6) (pow.f64 (.f64 4 (.f64 a c)) 3)) (+.f64 (pow.f64 b 4) (.f64 4 (.f64 (.f64 a c) (+.f64 (.f64 b b) (.f64 4 (.f64 a c)))))))
520.0ms	(+.f64 (pow.f64 b 4) (.f64 4 (.f64 (.f64 a c) (+.f64 (.f64 b b) (.f64 4 (.f64 a c))))))
309.0ms	(sqrt.f64 (/.f64 (-.f64 (pow.f64 b 6) (pow.f64 (.f64 4 (.f64 a c)) 3)) (+.f64 (pow.f64 b 4) (.f64 4 (.f64 (.f64 a c) (+.f64 (.f64 b b) (.f64 4 (.f64 a c))))))))
285.0ms	(.f64 (.f64 a c) (+.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 3398 to 2805 computations (17.5% saved)

simplify136.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

227 → 227

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5005	10596

localize21.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
0.0b	(.f64 4 (.f64 a c))
0.0b	(.f64 4 (.f64 a c))
0.0b	(.f64 4 (.f64 a c))
0.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
20.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
20.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
20.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite28.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_1123`
9×	`sqrt-prod_binary64_1117`
7×	`*-un-lft-identity_binary64_1101` `pow1_binary64_1162` `add-cube-cbrt_binary64_1136`
6×	`add-log-exp_binary64_1140` `sqrt-div_binary64_1118`
4×	`add-exp-log_binary64_1139` `flip--_binary64_1076` `flip3--_binary64_1105` `add-cbrt-cube_binary64_1137`
3×	`rem-sqrt-square_binary64_1114` `sqrt-pow1_binary64_1119` `pow1/2_binary64_1181`
1×	`diff-log_binary64_1193` `sub-neg_binary64_1094` `cancel-sign-sub-inv_binary64_1067`

Counts

4 → 57

Calls

8 calls:

5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
0.0ms	(.f64 4 (.f64 a c))

series746.0ms (0.6%)

Counts

4 → 75

Calls

4 calls:

193.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
187.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
184.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
182.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 6487 to 4449 computations (31.4% saved)

simplify94.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4939	2196
1	4939	2196

prune22.3s (17.4%)

Pruning

634 alts after pruning (618 fresh and 16 done)

	Pruned	Kept	Total
New	433	182	615
Fresh	12	436	448
Picked	0	0	0
Done	0	16	16
Total	445	634	1079

Error

3.3b

Counts

1079 → 634

Compiler

Compiled 15071 to 8521 computations (43.5% saved)

simplify805.0ms (0.6%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5117	59975

regimes30.1s (23.4%)

Compiler: Compiled 138710 to 95584 computations (31.1% saved)

bsearch156.0ms (0.1%)

Steps

Iters	Range		Point
6	9.213557312983252e+57	6.696592013615625e+58	6.584163964176897e+58
9	-2.3983360836152257e-251	-5.538899681204924e-257	-8.356600830588859e-253
8	-78.0306546130345	-0.007096600591868866	-0.12367712522464153

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes1.3s (1%)

Compiler: Compiled 4226 to 3656 computations (13.5% saved)

bsearch88.0ms (0.1%)

Steps

Iters	Range		Point
6	9.213557312983252e+57	6.696592013615625e+58	6.584163964176897e+58
8	-4.542050213126364e-133	-1.3383713089496891e-135	-3.3145832091508264e-133
8	-78.0306546130345	-0.007096600591868866	-6.950881560457148

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes1.2s (1%)

Compiler: Compiled 4138 to 3592 computations (13.2% saved)

bsearch53.0ms (0%)

Steps

Iters	Range		Point
6	9.213557312983252e+57	6.696592013615625e+58	6.584163964176897e+58
8	-2.317338217213781e-99	-4.3399739558858115e-102	-1.7658993441531842e-99

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes1.1s (0.8%)

Compiler: Compiled 3310 to 2920 computations (11.8% saved)

bsearch55.0ms (0%)

Steps

Iters	Range		Point
6	9.213557312983252e+57	6.696592013615625e+58	2.3018188694599006e+58
8	-2.317338217213781e-99	-4.3399739558858115e-102	-2.22034042432551e-99

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes605.0ms (0.5%)

Compiler: Compiled 1470 to 1362 computations (7.3% saved)

bsearch64.0ms (0%)

Steps

Iters	Range		Point
8	3.463029469069573e-28	1.6172222127559756e-23	1.3902737789955247e-26
8	-2.317338217213781e-99	-4.3399739558858115e-102	-1.7968403855442245e-100

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes443.0ms (0.3%)

Compiler: Compiled 1020 to 969 computations (5% saved)

bsearch60.0ms (0%)

Steps

Iters	Range		Point
8	3.463029469069573e-28	1.6172222127559756e-23	3.5241943098311867e-28
8	-2.317338217213781e-99	-4.3399739558858115e-102	-1.798231941782608e-99

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes324.0ms (0.3%)

Compiler: Compiled 924 to 876 computations (5.2% saved)

bsearch31.0ms (0%)

Steps

Iters	Range		Point
8	-1.301037189519903e-299	-5.4913144674176636e-303	-5.555147341543503e-303

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes137.0ms (0.1%)

Compiler: Compiled 192 to 255 computations (-32.8% saved)

bsearch40.0ms (0%)

Steps

Iters	Range		Point
10	-1.9776492919123162e-230	-4.9115895737932197e-244	-8.816227157884985e-240

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes29.0ms (0%)

Compiler: Compiled 27 to 69 computations (-155.6% saved)

bsearch0.0ms (0%)

regimes25.0ms (0%)

Accuracy

Total 5.9b remaining (63.4%)

Threshold costs 0b (0%)

Compiler

Compiled 15 to 54 computations (-260% saved)

bsearch12.0ms (0%)

Compiler: Compiled 277 to 196 computations (29.2% saved)

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	165	413
1	165	413

end0.0ms (0%)

sample30.5s (23.7%)

Algorithm

1×

intervals

Results

287.0ms	1167×	body	2048	valid
265.0ms	5106×	body	128	valid
152.0ms	763×	body	1024	valid
122.0ms	403×	body	4096	valid
55.0ms	385×	body	512	valid
37.0ms	732×	body	128	nan
21.0ms	410×	body	128	invalid
17.0ms	176×	body	256	valid

Compiler

Compiled 35545 to 24504 computations (31.1% saved)

Pareto

0.64264731321536