Details

analyze463.0ms (6.5%)

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)

sample41.0ms (0.6%)

Algorithm

1×

intervals

Results

9.0ms	172×	body	128	valid
8.0ms	32×	body	2048	valid
4.0ms	16×	body	512	valid
4.0ms	20×	body	1024	valid
3.0ms	11×	body	4096	valid
1.0ms	27×	body	128	nan
1.0ms	16×	body	128	invalid
0.0ms	5×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify404.0ms (5.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (313.0ms)

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

Merged error: 33.3b

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 (.f64 4 a) c))) b) (.f64 a 2))
0.4b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
1.1b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
21.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite38.0ms (0.5%)

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 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
11.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series262.0ms (3.7%)

Counts

4 → 12

Calls

4 calls:

103.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
62.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
60.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
37.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify95.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4899	1979
1	4899	1979

prune117.0ms (1.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	80	6	86
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	80	7	87

Merged error: 6.2b

Counts

87 → 7

Compiler

Compiled 2070 to 1232 computations (40.5% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b) 2)))
0.4b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
1.1b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
21.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite97.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

693×	`times-frac_binary64_1107`
439×	`add-sqr-sqrt_binary64_1123`
364×	`*-un-lft-identity_binary64_1101`
290×	`add-cube-cbrt_binary64_1136`
74×	`difference-of-squares_binary64_1070`
71×	`associate-/r*_binary64_1045`
40×	`sqrt-prod_binary64_1117`
37×	`distribute-lft-out--_binary64_1053`
25×	`add-exp-log_binary64_1139`
17×	`div-inv_binary64_1098`
15×	`div-exp_binary64_1152`
13×	`add-cbrt-cube_binary64_1137`
8×	`add-log-exp_binary64_1140`
6×	`pow1_binary64_1162` `cbrt-undiv_binary64_1135`
5×	`associate-/r/_binary64_1047`
4×	`cancel-sign-sub-inv_binary64_1067`
3×	`1-exp_binary64_1145` `flip--_binary64_1076` `flip3--_binary64_1105` `associate-/l*_binary64_1046` `rec-exp_binary64_1151`
2×	`diff-log_binary64_1193` `sub-neg_binary64_1094` `sqrt-div_binary64_1118`
1×	`inv-pow_binary64_1186` `rem-sqrt-square_binary64_1114` `frac-2neg_binary64_1112` `sqrt-pow1_binary64_1119` `clear-num_binary64_1100` `pow-flip_binary64_1175` `pow1/2_binary64_1181`

Counts

4 → 356

Calls

4 calls:

23.0ms	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b) 2)))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series282.0ms (4%)

Counts

4 → 12

Calls

4 calls:

126.0ms	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b) 2)))
65.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
56.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
35.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify196.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

368 → 368

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4968	16295
1	4968	16295

prune798.0ms (11.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	366	2	368
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	366	9	375

Merged error: 6.2b

Counts

375 → 9

Compiler

Compiled 12728 to 7686 computations (39.6% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.3b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
3.2b	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
10.6b	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
21.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite46.0ms (0.6%)

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 (.f64 4 a) c))))) (.f64 a 2))
11.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series470.0ms (6.6%)

Counts

4 → 12

Calls

4 calls:

192.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
158.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
60.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
59.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify98.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4956	3121
1	4956	3121

prune137.0ms (1.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	112	2	114
Fresh	2	4	6
Picked	1	0	1
Done	0	2	2
Total	115	8	123

Merged error: 6.2b

Counts

123 → 8

Compiler

Compiled 3216 to 1976 computations (38.6% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
0.4b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
1.3b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
21.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite28.0ms (0.4%)

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

series316.0ms (4.4%)

Counts

4 → 12

Calls

4 calls:

166.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
58.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
58.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
34.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify76.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4891	1972
1	4891	1972

prune92.0ms (1.3%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	84	8	92

Merged error: 6.2b

Counts

92 → 8

Compiler

Compiled 2137 to 1308 computations (38.8% saved)

regimes853.0ms (11.9%)

Compiler: Compiled 4080 to 3148 computations (22.8% saved)

bsearch112.0ms (1.6%)

Steps

Iters	Range	Point
9	7.219295201900938e+58	2.43651205626012e+64	2.4128408816895354e+64
9	-1.2620066309661761e-304	7.831385335596643e-308	-2.460485954681045e-307
10	-2.6930881658428087e+160	-4.4990338465426374e+148	-5.9369607730911e+148

Iters

Range

Point

7.219295201900938e+58

2.43651205626012e+64

2.4128408816895354e+64

-1.2620066309661761e-304

7.831385335596643e-308

-2.460485954681045e-307

-2.6930881658428087e+160

-4.4990338465426374e+148

-5.9369607730911e+148

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	105	82
1	105	82

end0.0ms (0%)

sample2.1s (28.9%)

Algorithm

1×

intervals

Results

288.0ms	1151×	body	2048	valid
269.0ms	5236×	body	128	valid
144.0ms	693×	body	1024	valid
120.0ms	395×	body	4096	valid
49.0ms	341×	body	512	valid
36.0ms	684×	body	128	nan
18.0ms	347×	body	128	invalid
18.0ms	184×	body	256	valid

Compiler

Compiled 1112 to 845 computations (24% saved)

Details

analyze463.0ms (6.5%)

sample41.0ms (0.6%)

simplify404.0ms (5.7%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

rewrite38.0ms (0.5%)

series262.0ms (3.7%)

simplify95.0ms (1.3%)

prune117.0ms (1.6%)

localize12.0ms (0.2%)

rewrite97.0ms (1.4%)

series282.0ms (4%)

simplify196.0ms (2.7%)

prune798.0ms (11.2%)

localize15.0ms (0.2%)

rewrite46.0ms (0.6%)

series470.0ms (6.6%)

simplify98.0ms (1.4%)

prune137.0ms (1.9%)

localize13.0ms (0.2%)

rewrite28.0ms (0.4%)

series316.0ms (4.4%)

simplify76.0ms (1.1%)

prune92.0ms (1.3%)

regimes853.0ms (11.9%)

bsearch112.0ms (1.6%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample2.1s (28.9%)

Profiling