Details

analyze6.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	50%	0%	4
75%	25%	0%	5
87.5%	12.5%	0%	6
93.7%	6.2%	0%	7
96.8%	3.1%	0%	8
98.4%	1.6%	0%	9
99.2%	0.8%	0%	10
99.6%	0.4%	0%	11
99.8%	0.2%	0%	12
99.9%	0.1%	0%	13
99.9%	0.1%	0.1%	14

Compiler

Compiled 16 to 14 computations (12.5% saved)

sample24.0ms (0.5%)

Algorithm

1×

intervals

Results

5.0ms	54×	body	512	valid
5.0ms	40×	body	1024	valid
5.0ms	128×	body	128	valid
2.0ms	34×	body	256	valid

Compiler

Compiled 31 to 28 computations (9.7% saved)

simplify103.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	192	22
1	192	22

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

11.0b

Counts

2 → 1

Compiler

Compiled 30 to 26 computations (13.3% saved)

localize13.0ms (0.3%)

Local error

Found 8 expressions with local error:

2.1b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
0.0b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
0.0b	(/.f64 1 (-.f64 x 1))
0.0b	(/.f64 1 (+.f64 x 1))
0.0b	(/.f64 1 (+.f64 x 1))
0.0b	(/.f64 1 (-.f64 x 1))
0.0b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
2.1b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

rewrite91.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

112×	`*-un-lft-identity_binary64_1101`
74×	`times-frac_binary64_1107`
72×	`add-sqr-sqrt_binary64_1123`
39×	`add-cube-cbrt_binary64_1136`
26×	`cancel-sign-sub-inv_binary64_1067`
18×	`distribute-lft-out--_binary64_1053`
17×	`distribute-lft-out_binary64_1052`
14×	`difference-of-squares_binary64_1070` `associate-+l+_binary64_1034`
12×	`add-exp-log_binary64_1139`
11×	`add-log-exp_binary64_1140` `associate-/r*_binary64_1045`
10×	`div-inv_binary64_1098`
8×	`add-cbrt-cube_binary64_1137`
6×	`pow1_binary64_1162` `associate-/l*_binary64_1046`
4×	`difference-of-sqr-1_binary64_1071` `associate-/r/_binary64_1047` `div-exp_binary64_1152`
3×	`flip--_binary64_1076` `flip3--_binary64_1105` `frac-add_binary64_1109`
2×	`inv-pow_binary64_1186` `diff-log_binary64_1193` `1-exp_binary64_1145` `frac-2neg_binary64_1112` `sum-log_binary64_1192` `sub-neg_binary64_1094` `clear-num_binary64_1100` `flip3-+_binary64_1104` `rec-exp_binary64_1151` `frac-sub_binary64_1110` `cbrt-undiv_binary64_1135` `flip-+_binary64_1075` `pow-flip_binary64_1175`
1×	`associate-+l-_binary64_1036` `+-commutative_binary64_1031`

Counts

4 → 161

Calls

8 calls:

41.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
19.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
11.0ms	(/.f64 1 (-.f64 x 1))
5.0ms	(/.f64 1 (+.f64 x 1))
0.0ms	(/.f64 1 (+.f64 x 1))

series192.0ms (4.3%)

Counts

4 → 47

Calls

4 calls:

96.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
38.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
29.0ms	(/.f64 1 (+.f64 x 1))
29.0ms	(/.f64 1 (-.f64 x 1))

Compiler

Compiled 880 to 759 computations (13.8% saved)

simplify98.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

208 → 208

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4938	3281
1	4938	3281

prune303.0ms (6.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	205	3	208
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	206	3	209

Error

0.3b

Counts

209 → 3

Compiler

Compiled 4190 to 3328 computations (20.6% saved)

localize17.0ms (0.4%)

Local error

Found 8 expressions with local error:

0.0b	(-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x))
0.0b	(/.f64 1 (+.f64 1 x))
0.0b	(/.f64 1 (+.f64 1 x))
0.0b	(/.f64 1 (+.f64 1 x))
0.1b	(+.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x))
0.1b	(+.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x))
6.2b	(+.f64 (*.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)) (-.f64 x 1)) 1)
12.8b	(/.f64 (.f64 (+.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)) (+.f64 (.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)) (-.f64 x 1)) 1)) (*.f64 (-.f64 x 1) (+.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x))))

rewrite154.0ms (3.5%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`*-un-lft-identity_binary64_1101`
16×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
13×	`flip3-+_binary64_1104` `flip-+_binary64_1075`
12×	`frac-times_binary64_1111`
11×	`associate-/l/_binary64_1048` `associate-/r/_binary64_1047`
10×	`add-log-exp_binary64_1140` `distribute-lft-out_binary64_1052`
9×	`times-frac_binary64_1107`
8×	`frac-add_binary64_1109` `associate-+l+_binary64_1034`
6×	`add-sqr-sqrt_binary64_1123` `add-cube-cbrt_binary64_1136` `cancel-sign-sub-inv_binary64_1067`
5×	`associate-r/_binary64_1043` `associate-l/_binary64_1044`
4×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `pow1_binary64_1162` `distribute-lft-in_binary64_1050` `flip--_binary64_1076` `flip3--_binary64_1105` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `distribute-rgt-in_binary64_1051`
3×	`sum-log_binary64_1192` `div-inv_binary64_1098` `+-commutative_binary64_1031`
2×	`sub-neg_binary64_1094`
1×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/l_binary64_1046` `associate-/r_binary64_1045`

Counts

4 → 94

Calls

8 calls:

75.0ms	(/.f64 (.f64 (+.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)) (+.f64 (.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)) (-.f64 x 1)) 1)) (*.f64 (-.f64 x 1) (+.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x))))
26.0ms	(+.f64 (*.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)) (-.f64 x 1)) 1)
18.0ms	(+.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x))
18.0ms	(+.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x))
0.0ms	(/.f64 1 (+.f64 1 x))

series279.0ms (6.3%)

Counts

4 → 47

Calls

4 calls:

121.0ms	(/.f64 (.f64 (+.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)) (+.f64 (.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)) (-.f64 x 1)) 1)) (*.f64 (-.f64 x 1) (+.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x))))
68.0ms	(+.f64 (*.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)) (-.f64 x 1)) 1)
47.0ms	(+.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x))
43.0ms	(+.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x))

Compiler

Compiled 1673 to 1406 computations (16% saved)

simplify89.0ms (2%)

Algorithm

1×	egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4936	3755
1	4936	3755

prune361.0ms (8.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	140	1	141
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	140	4	144

Error

0.0b

Counts

144 → 4

Compiler

Compiled 6040 to 4761 computations (21.2% saved)

localize12.0ms (0.3%)

Local error

Found 8 expressions with local error:

16.8b	(+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x)))
0.0b	(/.f64 (+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x))) (-.f64 (pow.f64 x 3) x))
0.0b	(-.f64 x (*.f64 (+.f64 1 x) 2))
0.0b	(*.f64 x (+.f64 1 x))
0.0b	(*.f64 x (+.f64 1 x))
0.0b	(/.f64 (+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x))) (-.f64 (pow.f64 x 3) x))
0.0b	(-.f64 x (*.f64 (+.f64 1 x) 2))
16.8b	(+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x)))

rewrite64.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`add-sqr-sqrt_binary64_1123`
42×	`associate-*r/_binary64_1043`
34×	`*-un-lft-identity_binary64_1101`
32×	`frac-add_binary64_1109`
27×	`times-frac_binary64_1107`
26×	`flip--_binary64_1076` `flip3--_binary64_1105`
20×	`add-cube-cbrt_binary64_1136`
19×	`flip3-+_binary64_1104` `flip-+_binary64_1075`
18×	`associate-/l/_binary64_1048`
16×	`difference-of-squares_binary64_1070` `frac-times_binary64_1111`
9×	`associate-/r*_binary64_1045`
8×	`add-log-exp_binary64_1140` `add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137` `associate-*l/_binary64_1044`
6×	`pow1_binary64_1162`
4×	`cube-prod_binary64_1129` `unpow-prod-down_binary64_1180` `distribute-rgt-out--_binary64_1055` `distribute-lft-in_binary64_1050` `distribute-lft-out--_binary64_1053` `unpow3_binary64_1167` `associate-r_binary64_1041` `sqr-pow_binary64_1073` `distribute-rgt-in_binary64_1051` `associate-+l+_binary64_1034`
3×	`sub-neg_binary64_1094` `associate-/l_binary64_1046` `associate-l*_binary64_1042` `cancel-sign-sub-inv_binary64_1067`
2×	`associate-+r+_binary64_1033` `associate-/r/_binary64_1047`
1×	`diff-log_binary64_1193` `*-commutative_binary64_1032` `cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `distribute-lft-out_binary64_1052` `frac-2neg_binary64_1112` `sum-log_binary64_1192` `clear-num_binary64_1100` `div-inv_binary64_1098` `+-commutative_binary64_1031` `pow-prod-down_binary64_1172` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `unswap-sqr_binary64_1069`

Counts

4 → 139

Calls

8 calls:

21.0ms	(/.f64 (+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x))) (-.f64 (pow.f64 x 3) x))
12.0ms	(+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x)))
7.0ms	(*.f64 x (+.f64 1 x))
3.0ms	(-.f64 x (*.f64 (+.f64 1 x) 2))
0.0ms	(*.f64 x (+.f64 1 x))

series140.0ms (3.2%)

Counts

4 → 26

Calls

4 calls:

70.0ms	(/.f64 (+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x))) (-.f64 (pow.f64 x 3) x))
36.0ms	(*.f64 x (+.f64 1 x))
24.0ms	(-.f64 x (*.f64 (+.f64 1 x) 2))
9.0ms	(+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x)))

Compiler

Compiled 615 to 496 computations (19.3% saved)

simplify110.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	6051	6218

prune358.0ms (8.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	164	1	165
Fresh	1	1	2
Picked	1	0	1
Done	1	0	1
Total	167	2	169

Error

0.0b

Counts

169 → 2

Compiler

Compiled 6653 to 4645 computations (30.2% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.3b	(/.f64 2 (-.f64 (pow.f64 x 3) x))
0.3b	(/.f64 2 (-.f64 (pow.f64 x 3) x))

rewrite14.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`add-sqr-sqrt_binary64_1123`
27×	`*-un-lft-identity_binary64_1101` `times-frac_binary64_1107`
16×	`difference-of-squares_binary64_1070`
15×	`add-cube-cbrt_binary64_1136`
9×	`associate-/r*_binary64_1045`
4×	`cube-prod_binary64_1129` `unpow-prod-down_binary64_1180` `distribute-rgt-out--_binary64_1055` `distribute-lft-out--_binary64_1053` `unpow3_binary64_1167` `sqr-pow_binary64_1073`
3×	`add-exp-log_binary64_1139` `associate-/l*_binary64_1046` `add-cbrt-cube_binary64_1137`
2×	`associate-/r/_binary64_1047`
1×	`add-log-exp_binary64_1140` `frac-2neg_binary64_1112` `pow1_binary64_1162` `clear-num_binary64_1100` `flip--_binary64_1076` `flip3--_binary64_1105` `div-inv_binary64_1098` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135`

Counts

1 → 53

Calls

2 calls:

9.0ms	(/.f64 2 (-.f64 (pow.f64 x 3) x))
0.0ms	(/.f64 2 (-.f64 (pow.f64 x 3) x))

series67.0ms (1.5%)

Counts

1 → 11

Calls

1 calls:

67.0ms

(/.f64 2 (-.f64 (pow.f64 x 3) x))

Compiler

Compiled 199 to 181 computations (9% saved)

simplify57.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4925	1199
1	4925	1199

prune70.0ms (1.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	60	4	64
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	61	5	66

Error

0.0b

Counts

66 → 5

Compiler

Compiled 951 to 707 computations (25.7% saved)

simplify22.0ms (0.5%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	375	1335
1	375	1335

regimes84.0ms (1.9%)

Compiler: Compiled 894 to 741 computations (17.1% saved)

bsearch0.0ms (0%)

regimes22.0ms (0.5%)

Compiler: Compiled 17 to 19 computations (-11.8% saved)

bsearch32.0ms (0.7%)

Steps

Iters	Range		Point
12	2.530455945396232e-27	954620873126964.6	0.4982984274889607
8	-3.221532685900676	-0.00074960793291294	-0.9916973497488216

Compiler

Compiled 1 to 1 computations (0% saved)

regimes20.0ms (0.5%)

Compiler: Compiled 8 to 11 computations (-37.5% saved)

bsearch31.0ms (0.7%)

Steps

Iters	Range		Point
12	2.530455945396232e-27	954620873126964.6	1.0048841710211733
8	-3.221532685900676	-0.00074960793291294	-0.9916973497488216

Compiler

Compiled 1 to 1 computations (0% saved)

regimes7.0ms (0.2%)

Accuracy

Total 0.1b remaining (95.8%)

Threshold costs 0.1b (95.8%)

Compiler

Compiled 5 to 8 computations (-60% saved)

bsearch3.0ms (0.1%)

Compiler: Compiled 45 to 39 computations (13.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	63
1	34	63

end0.0ms (0%)

sample1.6s (35.6%)

Algorithm

1×

intervals

Results

189.0ms	1341×	body	1024	valid
161.0ms	4433×	body	128	valid
155.0ms	1493×	body	512	valid
53.0ms	733×	body	256	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 962 to 800 computations (16.8% saved)

Pareto

0.4040227599646101

Details

analyze6.0ms (0.1%)

sample24.0ms (0.5%)

simplify103.0ms (2.3%)

prune3.0ms (0.1%)

localize13.0ms (0.3%)

rewrite91.0ms (2.1%)

series192.0ms (4.3%)

simplify98.0ms (2.2%)

prune303.0ms (6.8%)

localize17.0ms (0.4%)

rewrite154.0ms (3.5%)

series279.0ms (6.3%)

simplify89.0ms (2%)

prune361.0ms (8.1%)

localize12.0ms (0.3%)

rewrite64.0ms (1.4%)

series140.0ms (3.2%)

simplify110.0ms (2.5%)

prune358.0ms (8.1%)

localize5.0ms (0.1%)

rewrite14.0ms (0.3%)

series67.0ms (1.5%)

simplify57.0ms (1.3%)

prune70.0ms (1.6%)

simplify22.0ms (0.5%)

regimes84.0ms (1.9%)

bsearch0.0ms (0%)

regimes22.0ms (0.5%)

bsearch32.0ms (0.7%)

regimes20.0ms (0.5%)

bsearch31.0ms (0.7%)

regimes7.0ms (0.2%)

bsearch3.0ms (0.1%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.6s (35.6%)

Profiling