Details

analyze2.0ms (0%)

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)

sample16.0ms (0%)

Algorithm

1×

intervals

Results

10.0ms

256×

body

128

valid

Compiler

Compiled 15 to 12 computations (20% saved)

simplify220.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (11.0ms)

Iter	Nodes	Cost
0	8	10
1	8	10

prune4.0ms (0%)

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: 15.5b

Counts

2 → 1

Compiler

Compiled 14 to 10 computations (28.6% saved)

localize20.0ms (0%)

Local error

Found 1 expressions with local error:

15.5b

(/.f64 x (+.f64 (*.f64 x x) 1))

rewrite30.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64_419` `times-frac_binary64_425` `add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441`
3×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `associate-/r_binary64_363` `associate-/l_binary64_364`
2×	`associate-/r/_binary64_365`
1×	`flip3-+_binary64_422` `clear-num_binary64_418` `add-log-exp_binary64_458` `div-inv_binary64_416` `frac-2neg_binary64_430` `flip-+_binary64_393` `pow1_binary64_480` `div-exp_binary64_470` `cbrt-undiv_binary64_453`

Counts

1 → 29

Calls

1 calls:

19.0ms

(/.f64 x (+.f64 (*.f64 x x) 1))

series132.0ms (0.2%)

Counts

1 → 3

Calls

1 calls:

132.0ms

(/.f64 x (+.f64 (*.f64 x x) 1))

simplify131.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 0 (106.0ms)

Iter	Nodes	Cost
0	5064	550

prune245.0ms (0.3%)

Pruning

22 alts after pruning (21 fresh and 1 done)

	Pruned	Kept	Total
New	11	21	32
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	11	22	33

Merged error: 0b

Counts

33 → 22

Compiler

Compiled 816 to 482 computations (40.9% saved)

localize18.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
0.0b	(/.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) 1))) (sqrt.f64 (+.f64 (.f64 x x) 1)))
15.4b	(sqrt.f64 (+.f64 (*.f64 x x) 1))
15.4b	(sqrt.f64 (+.f64 (*.f64 x x) 1))

rewrite148.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

288×	`times-frac_binary64_425`
164×	`add-sqr-sqrt_binary64_441`
162×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
156×	`sqrt-prod_binary64_435`
27×	`associate-/l*_binary64_364`
22×	`sqrt-div_binary64_436`
18×	`associate-/r/_binary64_365`
12×	`associate-/r*_binary64_363`
11×	`flip3-+_binary64_422` `flip-+_binary64_393` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
9×	`div-inv_binary64_416`
6×	`pow1_binary64_480`
4×	`add-log-exp_binary64_458` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
2×	`clear-num_binary64_418` `pow1/2_binary64_499` `frac-2neg_binary64_430` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432`
1×	`associate-/l/_binary64_366`

Counts

4 → 262

Calls

4 calls:

40.0ms	(/.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) 1))) (sqrt.f64 (+.f64 (.f64 x x) 1)))
15.0ms	(/.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
9.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))
9.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

series290.0ms (0.4%)

Counts

4 → 12

Calls

4 calls:

133.0ms	(/.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
59.0ms	(/.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) 1))) (sqrt.f64 (+.f64 (.f64 x x) 1)))
57.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))
41.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

simplify758.0ms (1%)

Algorithm

1×	egg-herbie

Counts

274 → 274

Iterations

Useful iterations: 0 (414.0ms)

Iter	Nodes	Cost
0	4918	8543
1	4918	8543

prune4.2s (5.6%)

Pruning

105 alts after pruning (103 fresh and 2 done)

	Pruned	Kept	Total
New	186	88	274
Fresh	5	15	20
Picked	0	1	1
Done	0	1	1
Total	191	105	296

Merged error: 0b

Counts

296 → 105

Compiler

Compiled 9649 to 5817 computations (39.7% saved)

localize14.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
0.0b	(/.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) 1))) (fabs.f64 (sqrt.f64 (+.f64 (.f64 x x) 1))))
15.4b	(sqrt.f64 (+.f64 (*.f64 x x) 1))
15.4b	(sqrt.f64 (+.f64 (*.f64 x x) 1))

rewrite99.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

162×	`times-frac_binary64_425`
100×	`add-sqr-sqrt_binary64_441`
98×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
54×	`sqrt-prod_binary64_435`
27×	`associate-/l*_binary64_364`
14×	`sqrt-div_binary64_436`
11×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
10×	`associate-/r/_binary64_365`
9×	`associate-/r*_binary64_363`
7×	`flip3-+_binary64_422` `flip-+_binary64_393`
6×	`div-inv_binary64_416` `pow1_binary64_480`
4×	`add-log-exp_binary64_458` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
2×	`clear-num_binary64_418` `pow1/2_binary64_499` `frac-2neg_binary64_430` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432`
1×	`associate-/l/_binary64_366`

Counts

4 → 185

Calls

4 calls:

25.0ms	(/.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) 1))) (fabs.f64 (sqrt.f64 (+.f64 (.f64 x x) 1))))
13.0ms	(/.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
9.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))
7.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

series521.0ms (0.7%)

Counts

4 → 12

Calls

4 calls:

327.0ms	(/.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) 1))) (fabs.f64 (sqrt.f64 (+.f64 (.f64 x x) 1))))
128.0ms	(/.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
34.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))
31.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

simplify468.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

197 → 197

Iterations

Useful iterations: 0 (258.0ms)

Iter	Nodes	Cost
0	4923	5476
1	4923	5476

prune2.8s (3.7%)

Pruning

126 alts after pruning (123 fresh and 3 done)

	Pruned	Kept	Total
New	163	34	197
Fresh	13	89	102
Picked	0	1	1
Done	0	2	2
Total	176	126	302

Merged error: 0b

Counts

302 → 126

Compiler

Compiled 8253 to 5119 computations (38% saved)

localize16.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 x (.f64 1 (sqrt.f64 (+.f64 (.f64 x x) 1))))
0.0b	(/.f64 (/.f64 x (.f64 1 (sqrt.f64 (+.f64 (.f64 x x) 1)))) (fabs.f64 (sqrt.f64 (+.f64 (*.f64 x x) 1))))
15.4b	(sqrt.f64 (+.f64 (*.f64 x x) 1))
15.4b	(sqrt.f64 (+.f64 (*.f64 x x) 1))

rewrite69.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`times-frac_binary64_425`
28×	`add-sqr-sqrt_binary64_441`
26×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
23×	`add-exp-log_binary64_457`
18×	`add-cbrt-cube_binary64_455`
14×	`sqrt-div_binary64_436`
12×	`associate-/l*_binary64_364`
10×	`associate-*r/_binary64_361` `associate-/r/_binary64_365` `div-exp_binary64_470`
7×	`flip3-+_binary64_422` `flip-+_binary64_393` `cbrt-undiv_binary64_453`
6×	`div-inv_binary64_416` `sqrt-prod_binary64_435` `pow1_binary64_480`
4×	`add-log-exp_binary64_458` `prod-exp_binary64_468` `associate-/r*_binary64_363`
2×	`clear-num_binary64_418` `1-exp_binary64_463` `pow1/2_binary64_499` `cbrt-unprod_binary64_452` `frac-2neg_binary64_430` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432`
1×	`associate-/l/_binary64_366`

Counts

4 → 111

Calls

4 calls:

20.0ms	(/.f64 (/.f64 x (.f64 1 (sqrt.f64 (+.f64 (.f64 x x) 1)))) (fabs.f64 (sqrt.f64 (+.f64 (*.f64 x x) 1))))
15.0ms	(/.f64 x (.f64 1 (sqrt.f64 (+.f64 (.f64 x x) 1))))
8.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))
7.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

series386.0ms (0.5%)

Counts

4 → 12

Calls

4 calls:

198.0ms	(/.f64 (/.f64 x (.f64 1 (sqrt.f64 (+.f64 (.f64 x x) 1)))) (fabs.f64 (sqrt.f64 (+.f64 (*.f64 x x) 1))))
130.0ms	(/.f64 x (.f64 1 (sqrt.f64 (+.f64 (.f64 x x) 1))))
29.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))
28.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

simplify312.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (207.0ms)

Iter	Nodes	Cost
0	5017	2708

prune2.9s (3.8%)

Pruning

133 alts after pruning (129 fresh and 4 done)

	Pruned	Kept	Total
New	107	16	123
Fresh	9	113	122
Picked	0	1	1
Done	0	3	3
Total	116	133	249

Merged error: 0b

Counts

249 → 133

Compiler

Compiled 2793 to 1711 computations (38.7% saved)

regimes5.2s (6.8%)

Compiler: Compiled 13516 to 9322 computations (31% saved)

bsearch36.9s (48.8%)

Steps

Iters	Range		Point
9	105.54063684618005	163862830.16416195	439.8864172703267
7	-3855042427.592394	-48718305.914616175	-495675560.2626342

Compiler

Compiled 1 to 1 computations (0% saved)

simplify48.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	50	49
1	50	49

end0.0ms (0%)

sample19.6s (26%)

Algorithm

1×

intervals

Results

398.0ms

8000×

body

128

valid

Compiler

Compiled 6926 to 4793 computations (30.8% saved)

Pareto

0.25829965660286175

Details

analyze2.0ms (0%)

sample16.0ms (0%)

simplify220.0ms (0.3%)

prune4.0ms (0%)

localize20.0ms (0%)

rewrite30.0ms (0%)

series132.0ms (0.2%)

simplify131.0ms (0.2%)

prune245.0ms (0.3%)

localize18.0ms (0%)

rewrite148.0ms (0.2%)

series290.0ms (0.4%)

simplify758.0ms (1%)

prune4.2s (5.6%)

localize14.0ms (0%)

rewrite99.0ms (0.1%)

series521.0ms (0.7%)

simplify468.0ms (0.6%)

prune2.8s (3.7%)

localize16.0ms (0%)

rewrite69.0ms (0.1%)

series386.0ms (0.5%)

simplify312.0ms (0.4%)

prune2.9s (3.8%)

regimes5.2s (6.8%)

bsearch36.9s (48.8%)

simplify48.0ms (0.1%)

end0.0ms (0%)

sample19.6s (26%)

Profiling