Details

analyze309.0ms (3.2%)

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
49.9%	49.9%	0.1%	3
49.9%	49.9%	0.1%	4
49.9%	49.9%	0.1%	5
74.9%	25%	0.1%	6
74.9%	25%	0.1%	7
74.9%	25%	0.1%	8
87.4%	12.5%	0.1%	9
87.4%	12.5%	0.1%	10
87.4%	12.5%	0.1%	11
93.6%	6.2%	0.1%	12
93.6%	6.2%	0.1%	13
93.6%	6.2%	0.1%	14

Compiler

Compiled 24 to 21 computations (12.5% saved)

sample122.0ms (1.3%)

Algorithm

1×

intervals

Results

32.0ms	185×	body	128	valid
29.0ms	29×	body	2048	valid
23.0ms	18×	body	4096	valid
12.0ms	15×	body	1024	valid
4.0ms	7×	body	512	valid
1.0ms	2×	body	256	valid

Compiler

Compiled 47 to 44 computations (6.4% saved)

simplify205.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (89.0ms)

Iter	Nodes	Cost
0	4970	33
1	4970	33

prune9.0ms (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

27.2b

Counts

2 → 1

Compiler

Compiled 42 to 34 computations (19% saved)

localize31.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (-.f64 A C) 2)
0.0b	(.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B)))) B)) PI.f64))
0.1b	(-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))
33.0b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

rewrite50.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64_1123`
25×	`*-un-lft-identity_binary64_1101`
18×	`add-cube-cbrt_binary64_1136`
13×	`associate-r_binary64_1041`
10×	`add-exp-log_binary64_1139` `times-frac_binary64_1107`
9×	`add-log-exp_binary64_1140` `add-cbrt-cube_binary64_1137` `cancel-sign-sub-inv_binary64_1067`
8×	`pow1_binary64_1162`
7×	`sqrt-prod_binary64_1117`
6×	`sqrt-div_binary64_1118`
5×	`unpow-prod-down_binary64_1180`
4×	`distribute-lft-out--_binary64_1053` `associate--l+_binary64_1038` `frac-sub_binary64_1110`
3×	`diff-log_binary64_1193` `difference-of-squares_binary64_1070` `flip--_binary64_1076` `flip3--_binary64_1105` `flip3-+_binary64_1104` `pow-unpow_binary64_1178` `flip-+_binary64_1075` `associate-l_binary64_1042`
2×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `sub-neg_binary64_1094` `unswap-sqr_binary64_1069`
1×	`-commutative_binary64_1032` `pow-exp_binary64_1169` `rem-sqrt-square_binary64_1114` `pow-pow_binary64_1173` `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` `sqr-pow_binary64_1073` `pow-to-exp_binary64_1170` `unpow2_binary64_1166` `associate--l-_binary64_1039` `pow1/2_binary64_1181`

Counts

4 → 98

Calls

4 calls:

17.0ms	(-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))
9.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
9.0ms	(.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B)))) B)) PI.f64))
5.0ms	(pow.f64 (-.f64 A C) 2)

series504.0ms (5.3%)

Counts

4 → 12

Calls

4 calls:

264.0ms	(.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B)))) B)) PI.f64))
107.0ms	(-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))
106.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
26.0ms	(pow.f64 (-.f64 A C) 2)

simplify79.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4968	2986
1	4968	2986

prune244.0ms (2.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	102	8	110
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	103	8	111

Error

18.4b

Counts

111 → 8

Compiler

Compiled 3467 to 1775 computations (48.8% saved)

localize31.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (-.f64 A C) 2)
0.0b	(/.f64 (.f64 180 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B)))) B))) PI.f64)
0.1b	(-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))
33.0b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

rewrite71.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64_1123` `*-un-lft-identity_binary64_1101`
12×	`add-cube-cbrt_binary64_1136`
10×	`add-exp-log_binary64_1139`
9×	`add-log-exp_binary64_1140` `add-cbrt-cube_binary64_1137` `cancel-sign-sub-inv_binary64_1067`
7×	`sqrt-prod_binary64_1117`
6×	`pow1_binary64_1162` `sqrt-div_binary64_1118`
5×	`unpow-prod-down_binary64_1180`
4×	`distribute-lft-out--_binary64_1053` `associate--l+_binary64_1038` `frac-sub_binary64_1110`
3×	`diff-log_binary64_1193` `difference-of-squares_binary64_1070` `flip--_binary64_1076` `flip3--_binary64_1105` `flip3-+_binary64_1104` `pow-unpow_binary64_1178` `times-frac_binary64_1107` `flip-+_binary64_1075` `associate-/r*_binary64_1045`
2×	`sub-neg_binary64_1094` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135`
1×	`pow-exp_binary64_1169` `rem-sqrt-square_binary64_1114` `cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `pow-pow_binary64_1173` `frac-2neg_binary64_1112` `sqrt-pow1_binary64_1119` `clear-num_binary64_1100` `div-inv_binary64_1098` `associate-/l*_binary64_1046` `sqr-pow_binary64_1073` `pow-to-exp_binary64_1170` `unpow2_binary64_1166` `associate--l-_binary64_1039` `pow1/2_binary64_1181`

Counts

4 → 87

Calls

4 calls:

32.0ms	(-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))
19.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
6.0ms	(/.f64 (.f64 180 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B)))) B))) PI.f64)
5.0ms	(pow.f64 (-.f64 A C) 2)

series359.0ms (3.7%)

Counts

4 → 12

Calls

4 calls:

173.0ms	(/.f64 (.f64 180 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B)))) B))) PI.f64)
90.0ms	(-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))
82.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
14.0ms	(pow.f64 (-.f64 A C) 2)

simplify68.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5066	2523

prune197.0ms (2.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	96	3	99
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	98	9	107

Error

18.4b

Counts

107 → 9

Compiler

Compiled 2938 to 1521 computations (48.2% saved)

localize30.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (-.f64 A C) 2)
0.0b	(/.f64 PI.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))) B)))
0.1b	(-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))
33.0b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

rewrite57.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64_1123` `*-un-lft-identity_binary64_1101`
18×	`add-cube-cbrt_binary64_1136`
9×	`add-log-exp_binary64_1140` `times-frac_binary64_1107` `cancel-sign-sub-inv_binary64_1067`
7×	`add-exp-log_binary64_1139` `sqrt-prod_binary64_1117`
6×	`pow1_binary64_1162` `add-cbrt-cube_binary64_1137` `sqrt-div_binary64_1118`
5×	`unpow-prod-down_binary64_1180`
4×	`distribute-lft-out--_binary64_1053` `associate--l+_binary64_1038` `frac-sub_binary64_1110`
3×	`diff-log_binary64_1193` `difference-of-squares_binary64_1070` `flip--_binary64_1076` `flip3--_binary64_1105` `flip3-+_binary64_1104` `pow-unpow_binary64_1178` `associate-/l_binary64_1046` `flip-+_binary64_1075` `associate-/r_binary64_1045`
2×	`sub-neg_binary64_1094`
1×	`pow-exp_binary64_1169` `rem-sqrt-square_binary64_1114` `pow-pow_binary64_1173` `frac-2neg_binary64_1112` `sqrt-pow1_binary64_1119` `clear-num_binary64_1100` `div-inv_binary64_1098` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `sqr-pow_binary64_1073` `pow-to-exp_binary64_1170` `unpow2_binary64_1166` `associate--l-_binary64_1039` `pow1/2_binary64_1181`

Counts

4 → 93

Calls

4 calls:

21.0ms	(-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))
16.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
6.0ms	(/.f64 PI.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))) B)))
5.0ms	(pow.f64 (-.f64 A C) 2)

series407.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

211.0ms	(/.f64 PI.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))) B)))
97.0ms	(-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))
79.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
20.0ms	(pow.f64 (-.f64 A C) 2)

simplify96.0ms (1%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4968	2979
1	4968	2979

prune198.0ms (2.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	103	2	105
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	106	8	114

Error

18.4b

Counts

114 → 8

Compiler

Compiled 3297 to 1683 computations (49% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 180 (atan.f64 (/.f64 (-.f64 C (+.f64 A (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B))))) B)))
0.1b	(/.f64 (.f64 180 (atan.f64 (/.f64 (-.f64 C (+.f64 A (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B))))) B))) PI.f64)
1.0b	(+.f64 A (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))
33.0b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

rewrite60.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64_1123`
11×	`*-un-lft-identity_binary64_1101` `add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
9×	`add-cube-cbrt_binary64_1136`
7×	`pow1_binary64_1162`
6×	`add-log-exp_binary64_1140`
3×	`sqrt-prod_binary64_1117` `times-frac_binary64_1107` `associate-r_binary64_1041` `associate-l_binary64_1042` `associate-/r*_binary64_1045`
2×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `flip3-+_binary64_1104` `sqrt-div_binary64_1118` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `flip-+_binary64_1075`
1×	`-commutative_binary64_1032` `rem-sqrt-square_binary64_1114` `distribute-lft-out_binary64_1052` `frac-2neg_binary64_1112` `sum-log_binary64_1192` `sqrt-pow1_binary64_1119` `clear-num_binary64_1100` `div-inv_binary64_1098` `associate-/l_binary64_1046` `+-commutative_binary64_1031` `pow-prod-down_binary64_1172` `unswap-sqr_binary64_1069` `pow1/2_binary64_1181`

Counts

4 → 66

Calls

4 calls:

23.0ms	(+.f64 A (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))
15.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
9.0ms	(/.f64 (.f64 180 (atan.f64 (/.f64 (-.f64 C (+.f64 A (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B))))) B))) PI.f64)
7.0ms	(.f64 180 (atan.f64 (/.f64 (-.f64 C (+.f64 A (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B))))) B)))

series441.0ms (4.6%)

Counts

4 → 12

Calls

4 calls:

143.0ms	(/.f64 (.f64 180 (atan.f64 (/.f64 (-.f64 C (+.f64 A (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B))))) B))) PI.f64)
119.0ms	(+.f64 A (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))
106.0ms	(.f64 180 (atan.f64 (/.f64 (-.f64 C (+.f64 A (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B))))) B)))
73.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

simplify82.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5097	2197

prune145.0ms (1.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	72	6	78
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	74	12	86

Error

18.4b

Counts

86 → 12

Compiler

Compiled 2136 to 1176 computations (44.9% saved)

regimes916.0ms (9.5%)

Accuracy

Total 5.4b remaining (22.1%)

Threshold costs 0b (0%)

Compiler

Compiled 7553 to 5504 computations (27.1% saved)

bsearch67.0ms (0.7%)

Steps

Iters	Range		Point
10	1.704313321832674e+140	1.9288246449212064e+154	1.314127621982934e+154

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	63	58
1	63	58

end0.0ms (0%)

sample4.8s (50%)

Algorithm

1×

intervals

Results

987.0ms	835×	body	4096	valid
823.0ms	5410×	body	128	valid
743.0ms	869×	body	2048	valid
343.0ms	508×	body	1024	valid
123.0ms	253×	body	512	valid
37.0ms	125×	body	256	valid

Compiler

Compiled 1116 to 814 computations (27.1% saved)

Details

analyze309.0ms (3.2%)

sample122.0ms (1.3%)

simplify205.0ms (2.1%)

prune9.0ms (0.1%)

localize31.0ms (0.3%)

rewrite50.0ms (0.5%)

series504.0ms (5.3%)

simplify79.0ms (0.8%)

prune244.0ms (2.5%)

localize31.0ms (0.3%)

rewrite71.0ms (0.7%)

series359.0ms (3.7%)

simplify68.0ms (0.7%)

prune197.0ms (2.1%)

localize30.0ms (0.3%)

rewrite57.0ms (0.6%)

series407.0ms (4.2%)

simplify96.0ms (1%)

prune198.0ms (2.1%)

localize18.0ms (0.2%)

rewrite60.0ms (0.6%)

series441.0ms (4.6%)

simplify82.0ms (0.9%)

prune145.0ms (1.5%)

regimes916.0ms (9.5%)

bsearch67.0ms (0.7%)

simplify3.0ms (0%)

end0.0ms (0%)

sample4.8s (50%)

Profiling