Details

analyze1.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
100%	0%	0%	2

Compiler

Compiled 8 to 6 computations (25% saved)

sample15.0ms (0.6%)

Algorithm

1×

intervals

Results

9.0ms

256×

body

128

valid

Compiler

Compiled 15 to 12 computations (20% saved)

simplify158.0ms (6.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	8	10
1	8	10

prune2.0ms (0.1%)

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

Merged error: 14.4b

Counts

2 → 1

Compiler

Compiled 14 to 10 computations (28.6% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (*.f64 x x) 1)
14.4b	(/.f64 x (+.f64 (*.f64 x x) 1))

rewrite15.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64_1111` `add-sqr-sqrt_binary64_1133` `add-cube-cbrt_binary64_1146`
9×	`times-frac_binary64_1117`
4×	`add-cbrt-cube_binary64_1147` `add-log-exp_binary64_1150` `add-exp-log_binary64_1149`
3×	`associate-/r_binary64_1055` `associate-/l_binary64_1056`
2×	`flip-+_binary64_1085` `flip3-+_binary64_1114` `pow1_binary64_1172` `associate-/r/_binary64_1057`
1×	`div-inv_binary64_1108` `frac-2neg_binary64_1122` `+-commutative_binary64_1041` `div-exp_binary64_1162` `cbrt-undiv_binary64_1145` `sum-log_binary64_1202` `clear-num_binary64_1110`

Counts

2 → 40

Calls

2 calls:

7.0ms	(/.f64 x (+.f64 (*.f64 x x) 1))
5.0ms	(+.f64 (*.f64 x x) 1)

series100.0ms (3.9%)

Counts

2 → 6

Calls

2 calls:

54.0ms	(/.f64 x (+.f64 (*.f64 x x) 1))
46.0ms	(+.f64 (*.f64 x x) 1)

simplify65.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4989	689
1	4989	689

prune118.0ms (4.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	43	3	46
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	43	4	47

Merged error: 0b

Counts

47 → 4

Compiler

Compiled 1853 to 1150 computations (37.9% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
0.0b	(/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) 1)))
14.3b	(sqrt.f64 (+.f64 (*.f64 x x) 1))
14.3b	(sqrt.f64 (+.f64 (*.f64 x x) 1))

rewrite40.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64_1133`
36×	`times-frac_binary64_1117` `*-un-lft-identity_binary64_1111` `add-cube-cbrt_binary64_1146`
30×	`sqrt-prod_binary64_1127`
12×	`associate-/r*_binary64_1055`
10×	`add-exp-log_binary64_1149`
8×	`add-cbrt-cube_binary64_1147` `sqrt-div_binary64_1128` `pow1_binary64_1172`
6×	`associate-/l*_binary64_1056`
4×	`flip-+_binary64_1085` `flip3-+_binary64_1114` `add-log-exp_binary64_1150` `associate-/r/_binary64_1057`
3×	`pow1/2_binary64_1191` `pow-flip_binary64_1185` `div-exp_binary64_1162` `sqrt-pow1_binary64_1129`
2×	`rem-sqrt-square_binary64_1124` `div-inv_binary64_1108` `frac-2neg_binary64_1122` `cbrt-undiv_binary64_1145` `clear-num_binary64_1110`
1×	`1-exp_binary64_1155` `rec-exp_binary64_1161` `inv-pow_binary64_1196`

Counts

4 → 118

Calls

4 calls:

11.0ms	(/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) 1)))
8.0ms	(/.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
5.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))
5.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

series190.0ms (7.4%)

Counts

4 → 12

Calls

4 calls:

74.0ms	(/.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
47.0ms	(/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) 1)))
36.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))
33.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

simplify82.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4982	2284
1	4982	2284

prune149.0ms (5.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	130	0	130
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	130	4	134

Merged error: 0b

Counts

134 → 4

Compiler

Compiled 3134 to 1965 computations (37.3% saved)

localize8.0ms (0.3%)

Local error

Found 2 expressions with local error:

2.0b	(/.f64 x (+.f64 (pow.f64 x 4) -1))
20.4b	(.f64 (/.f64 x (+.f64 (pow.f64 x 4) -1)) (-.f64 (.f64 x x) 1))

rewrite44.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`add-sqr-sqrt_binary64_1133`
43×	`times-frac_binary64_1117` `*-un-lft-identity_binary64_1111`
28×	`add-cube-cbrt_binary64_1146`
27×	`associate-l_binary64_1052`
21×	`difference-of-sqr--1_binary64_1082`
9×	`add-cbrt-cube_binary64_1147` `add-exp-log_binary64_1149`
7×	`unpow-prod-down_binary64_1190` `associate-/r*_binary64_1055` `distribute-lft-out_binary64_1062` `sqr-pow_binary64_1083`
6×	`cancel-sign-sub-inv_binary64_1077` `associate-r_binary64_1051`
4×	`distribute-lft-in_binary64_1060` `distribute-rgt-in_binary64_1061` `pow1_binary64_1172` `associate-/r/_binary64_1057`
3×	`associate-/l*_binary64_1056`
2×	`prod-exp_binary64_1160` `cbrt-unprod_binary64_1144` `div-inv_binary64_1108` `flip-+_binary64_1085` `frac-times_binary64_1121` `flip3--_binary64_1115` `flip3-+_binary64_1114` `div-exp_binary64_1162` `cbrt-undiv_binary64_1145` `unswap-sqr_binary64_1079` `difference-of-squares_binary64_1080` `add-log-exp_binary64_1150` `sub-neg_binary64_1104` `flip--_binary64_1086` `associate-*r/_binary64_1053`
1×	`-commutative_binary64_1042` `associate-l/_binary64_1054` `frac-2neg_binary64_1122` `pow-prod-down_binary64_1182` `difference-of-sqr-1_binary64_1081` `clear-num_binary64_1110`

Counts

2 → 106

Calls

2 calls:

24.0ms	(.f64 (/.f64 x (+.f64 (pow.f64 x 4) -1)) (-.f64 (.f64 x x) 1))
9.0ms	(/.f64 x (+.f64 (pow.f64 x 4) -1))

series226.0ms (8.8%)

Counts

2 → 6

Calls

2 calls:

139.0ms	(/.f64 x (+.f64 (pow.f64 x 4) -1))
87.0ms	(.f64 (/.f64 x (+.f64 (pow.f64 x 4) -1)) (-.f64 (.f64 x x) 1))

simplify64.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4856	1938
1	4856	1938

prune113.0ms (4.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	112	4	116

Merged error: 0b

Counts

116 → 4

Compiler

Compiled 2202 to 1429 computations (35.1% saved)

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 5)))
0.2b	(pow.f64 (/.f64 1 x) 3)
0.5b	(/.f64 1 (pow.f64 x 5))
20.6b	(-.f64 (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 5))) (pow.f64 (/.f64 1 x) 3))

rewrite108.0ms (4.2%)

Algorithm

1×	rewrite-expression-head

Rules

74×	`*-un-lft-identity_binary64_1111`
69×	`add-sqr-sqrt_binary64_1133`
67×	`times-frac_binary64_1117`
52×	`add-cube-cbrt_binary64_1146`
41×	`unpow-prod-down_binary64_1190`
32×	`cancel-sign-sub-inv_binary64_1077`
29×	`cube-prod_binary64_1139`
18×	`add-exp-log_binary64_1149`
13×	`div-inv_binary64_1108`
11×	`add-log-exp_binary64_1150` `distribute-lft-out_binary64_1062`
9×	`add-cbrt-cube_binary64_1147`
8×	`div-exp_binary64_1162` `difference-of-squares_binary64_1080`
7×	`associate-/r*_binary64_1055` `pow-exp_binary64_1179` `sqr-pow_binary64_1083`
6×	`pow1_binary64_1172`
5×	`distribute-lft-out--_binary64_1063`
4×	`cube-div_binary64_1140` `1-exp_binary64_1155` `rec-exp_binary64_1161` `pow-to-exp_binary64_1180`
3×	`frac-sub_binary64_1120` `pow-unpow_binary64_1188` `associate-/l*_binary64_1056` `pow-pow_binary64_1183`
2×	`cube-mult_binary64_1141` `flip-+_binary64_1085` `pow-flip_binary64_1185` `diff-log_binary64_1203` `flip3-+_binary64_1114` `cbrt-undiv_binary64_1145` `frac-add_binary64_1119` `rem-cube-cbrt_binary64_1134` `unpow3_binary64_1177` `sum-log_binary64_1202` `inv-pow_binary64_1196`
1×	`frac-2neg_binary64_1122` `flip3--_binary64_1115` `+-commutative_binary64_1041` `associate--l+_binary64_1048` `sub-neg_binary64_1104` `clear-num_binary64_1110` `flip--_binary64_1086`

Counts

4 → 183

Calls

4 calls:

54.0ms	(-.f64 (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 5))) (pow.f64 (/.f64 1 x) 3))
23.0ms	(+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 5)))
6.0ms	(pow.f64 (/.f64 1 x) 3)
5.0ms	(/.f64 1 (pow.f64 x 5))

series240.0ms (9.3%)

Counts

4 → 12

Calls

4 calls:

101.0ms	(+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 5)))
56.0ms	(/.f64 1 (pow.f64 x 5))
42.0ms	(pow.f64 (/.f64 1 x) 3)
40.0ms	(-.f64 (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 5))) (pow.f64 (/.f64 1 x) 3))

simplify99.0ms (3.8%)

Algorithm

1×	egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4847	2892
1	4847	2892

prune243.0ms (9.4%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	195	0	195
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	195	4	199

Merged error: 0b

Counts

199 → 4

Compiler

Compiled 3917 to 3111 computations (20.6% saved)

regimes45.0ms (1.7%)

Compiler: Compiled 120 to 92 computations (23.3% saved)

bsearch1.0ms (0%)

Compiler: Compiled 7 to 5 computations (28.6% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	40	80
1	40	80

end0.0ms (0%)

sample422.0ms (16.4%)

Algorithm

1×

intervals

Results

174.0ms

8000×

body

128

valid

Compiler

Compiled 120 to 90 computations (25% saved)

Details

analyze1.0ms (0.1%)

sample15.0ms (0.6%)

simplify158.0ms (6.2%)

prune2.0ms (0.1%)

localize4.0ms (0.2%)

rewrite15.0ms (0.6%)

series100.0ms (3.9%)

simplify65.0ms (2.5%)

prune118.0ms (4.6%)

localize8.0ms (0.3%)

rewrite40.0ms (1.6%)

series190.0ms (7.4%)

simplify82.0ms (3.2%)

prune149.0ms (5.8%)

localize8.0ms (0.3%)

rewrite44.0ms (1.7%)

series226.0ms (8.8%)

simplify64.0ms (2.5%)

prune113.0ms (4.4%)

localize9.0ms (0.4%)

rewrite108.0ms (4.2%)

series240.0ms (9.3%)

simplify99.0ms (3.8%)

prune243.0ms (9.4%)

regimes45.0ms (1.7%)

bsearch1.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample422.0ms (16.4%)

Profiling