Details

analyze476.0ms (8.1%)

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)

sample40.0ms (0.7%)

Algorithm

1×

intervals

Results

8.0ms	161×	body	128	valid
8.0ms	33×	body	2048	valid
5.0ms	26×	body	1024	valid
4.0ms	14×	body	4096	valid
2.0ms	12×	body	512	valid
1.0ms	25×	body	128	nan
1.0ms	10×	body	256	valid
1.0ms	10×	body	128	invalid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify397.0ms (6.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (306.0ms)

Iter	Nodes	Cost
0	1834	24
1	1834	24

prune4.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

34.7b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
0.4b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.3b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
20.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite36.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_1123`
14×	`*-un-lft-identity_binary64_1101`
9×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
8×	`add-log-exp_binary64_1140` `add-cube-cbrt_binary64_1136`
6×	`difference-of-squares_binary64_1070` `sqrt-prod_binary64_1117` `associate-/l*_binary64_1046` `times-frac_binary64_1107`
5×	`pow1_binary64_1162`
4×	`flip--_binary64_1076` `flip3--_binary64_1105` `cancel-sign-sub-inv_binary64_1067`
3×	`distribute-lft-out--_binary64_1053`
2×	`diff-log_binary64_1193` `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` `clear-num_binary64_1100` `div-inv_binary64_1098` `associate-/r*_binary64_1045` `pow1/2_binary64_1181` `div-sub_binary64_1106`

Counts

4 → 74

Calls

4 calls:

12.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series265.0ms (4.5%)

Counts

4 → 12

Calls

4 calls:

103.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
63.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
61.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
37.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify103.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	4895	1979
1	4895	1979

prune111.0ms (1.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	79	7	86
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	7	87

Error

4.3b

Counts

87 → 7

Compiler

Compiled 2086 to 1138 computations (45.4% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.7b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
4.4b	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (.f64 a 2))
8.0b	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
20.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite50.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
22×	`times-frac_binary64_1107`
21×	`*-un-lft-identity_binary64_1101`
17×	`div-exp_binary64_1152` `cbrt-undiv_binary64_1135`
13×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150`
12×	`add-sqr-sqrt_binary64_1123`
11×	`add-cube-cbrt_binary64_1136` `associate-/l*_binary64_1046`
6×	`add-log-exp_binary64_1140` `associate-/r/_binary64_1047`
5×	`distribute-lft-out_binary64_1052` `pow1_binary64_1162` `associate-/r*_binary64_1045`
4×	`flip3-+_binary64_1104` `div-inv_binary64_1098` `flip-+_binary64_1075`
3×	`sqrt-prod_binary64_1117`
2×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `sqrt-div_binary64_1118`
1×	`rem-sqrt-square_binary64_1114` `sum-log_binary64_1192` `sqrt-pow1_binary64_1119` `flip--_binary64_1076` `flip3--_binary64_1105` `associate-/l/_binary64_1048` `+-commutative_binary64_1031` `pow1/2_binary64_1181`

Counts

4 → 102

Calls

4 calls:

14.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (.f64 a 2))
13.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
6.0ms	(+.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))))

series467.0ms (8%)

Counts

4 → 12

Calls

4 calls:

194.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
157.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (.f64 a 2))
60.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
56.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify75.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4959	3121
1	4959	3121

prune139.0ms (2.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	114	7	121

Error

4.2b

Counts

121 → 7

Compiler

Compiled 3228 to 1831 computations (43.3% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
0.4b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.7b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
20.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite30.0ms (0.5%)

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-/r*_binary64_1045`
3×	`sqrt-prod_binary64_1117` `associate-/l*_binary64_1046`
2×	`flip--_binary64_1076` `flip3--_binary64_1105` `flip3-+_binary64_1104` `associate-/r/_binary64_1047` `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

4 calls:

8.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series329.0ms (5.6%)

Counts

4 → 12

Calls

4 calls:

164.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
68.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
63.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
34.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify105.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	4896	1972
1	4896	1972

prune99.0ms (1.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	84	7	91

Error

4.2b

Counts

91 → 7

Compiler

Compiled 2226 to 1271 computations (42.9% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (/.f64 1/2 a))
0.4b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.3b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
20.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite39.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64_1123`
18×	`*-un-lft-identity_binary64_1101`
14×	`add-cube-cbrt_binary64_1136`
13×	`associate-r_binary64_1041`
10×	`times-frac_binary64_1107`
9×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
8×	`add-log-exp_binary64_1140`
7×	`pow1_binary64_1162`
6×	`associate-l_binary64_1042`
5×	`flip--_binary64_1076` `flip3--_binary64_1105` `sqrt-prod_binary64_1117`
4×	`difference-of-squares_binary64_1070` `cancel-sign-sub-inv_binary64_1067`
2×	`diff-log_binary64_1193` `cbrt-unprod_binary64_1134` `frac-times_binary64_1111` `prod-exp_binary64_1150` `sub-neg_binary64_1094` `distribute-lft-out--_binary64_1053` `sqrt-div_binary64_1118` `unswap-sqr_binary64_1069` `associate-*l/_binary64_1044`
1×	`-commutative_binary64_1032` `rem-sqrt-square_binary64_1114` `sqrt-pow1_binary64_1119` `associate-r/_binary64_1043` `div-inv_binary64_1098` `pow-prod-down_binary64_1172` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `pow1/2_binary64_1181`

Counts

4 → 83

Calls

4 calls:

15.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (/.f64 1/2 a))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series262.0ms (4.5%)

Counts

4 → 12

Calls

4 calls:

103.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (/.f64 1/2 a))
64.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
62.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
32.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify77.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5317	2202

prune97.0ms (1.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	95	0	95
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	95	7	102

Error

4.2b

Counts

102 → 7

Compiler

Compiled 2191 to 1178 computations (46.2% saved)

regimes499.0ms (8.5%)

Accuracy

Total 1.0b remaining (15%)

Threshold costs 1.0b (15%)

Compiler

Compiled 3136 to 2460 computations (21.6% saved)

bsearch102.0ms (1.7%)

Steps

Iters	Range	Point
7	1.8515760575460165e+108	7.079746839452132e+109	9.806096002062306e+108
9	3.471655958753961e-308	1.338164201957951e-301	7.151073671652035e-308
9	-3.203657050301464e+105	-6.409993448757428e+99	-3.161255245507665e+105

Iters

Range

Point

1.8515760575460165e+108

7.079746839452132e+109

9.806096002062306e+108

3.471655958753961e-308

1.338164201957951e-301

7.151073671652035e-308

-3.203657050301464e+105

-6.409993448757428e+99

-3.161255245507665e+105

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	105	82
1	105	82

end0.0ms (0%)

sample2.0s (34.1%)

Algorithm

1×

intervals

Results

306.0ms	5228×	body	128	valid
298.0ms	1110×	body	2048	valid
161.0ms	748×	body	1024	valid
129.0ms	390×	body	4096	valid
52.0ms	332×	body	512	valid
34.0ms	639×	body	128	nan
20.0ms	192×	body	256	valid
20.0ms	359×	body	128	invalid

Compiler

Compiled 876 to 671 computations (23.4% saved)

Details

analyze476.0ms (8.1%)

sample40.0ms (0.7%)

simplify397.0ms (6.8%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

rewrite36.0ms (0.6%)

series265.0ms (4.5%)

simplify103.0ms (1.8%)

prune111.0ms (1.9%)

localize15.0ms (0.2%)

rewrite50.0ms (0.9%)

series467.0ms (8%)

simplify75.0ms (1.3%)

prune139.0ms (2.4%)

localize15.0ms (0.3%)

rewrite30.0ms (0.5%)

series329.0ms (5.6%)

simplify105.0ms (1.8%)

prune99.0ms (1.7%)

localize11.0ms (0.2%)

rewrite39.0ms (0.7%)

series262.0ms (4.5%)

simplify77.0ms (1.3%)

prune97.0ms (1.7%)

regimes499.0ms (8.5%)

bsearch102.0ms (1.7%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample2.0s (34.1%)

Profiling