Details

analyze4.8s (11.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.2%	0.8%	0
0%	99.2%	0.8%	1
0%	99.2%	0.8%	2
0%	99.2%	0.8%	3
0%	99.2%	0.8%	4
0%	99.2%	0.8%	5
0%	99.2%	0.8%	6
0%	99.2%	0.8%	7
0%	99.2%	0.8%	8
0%	99.2%	0.8%	9
0%	99.2%	0.8%	10
0%	99.2%	0.8%	11
0%	99.2%	0.8%	12
0%	99.2%	0.8%	13
0%	99.2%	0.8%	14

Compiler

Compiled 96 to 64 computations (33.3% saved)

sample654.0ms (1.5%)

Algorithm

1×

intervals

Results

397.0ms	1967×	body	128	invalid
48.0ms	256×	body	128	valid

Compiler

Compiled 191 to 143 computations (25.1% saved)

simplify210.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5147	142

prune6.0ms (0%)

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

Merged error: 28.4b

Counts

2 → 1

Compiler

Compiled 190 to 126 computations (33.7% saved)

localize67.0ms (0.2%)

Local error

Found 4 expressions with local error:

8.6b	(.f64 (-.f64 (.f64 x y2) (.f64 z y3)) (-.f64 (.f64 y0 c) (*.f64 y1 a)))
9.6b	(.f64 (-.f64 (.f64 t y2) (.f64 y y3)) (-.f64 (.f64 y4 c) (*.f64 y5 a)))
10.0b	(.f64 (-.f64 (.f64 t j) (.f64 y k)) (-.f64 (.f64 y4 b) (*.f64 y5 i)))
12.1b	(.f64 (-.f64 (.f64 k y2) (.f64 j y3)) (-.f64 (.f64 y4 y1) (*.f64 y5 y0)))

rewrite84.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`flip3--_binary64_17627` `flip--_binary64_17598`
20×	`add-sqr-sqrt_binary64_17645`
16×	`frac-times_binary64_17633`
12×	`add-cbrt-cube_binary64_17659` `associate-l_binary64_17564` `associate-r_binary64_17563` `add-cube-cbrt_binary64_17658` `*-un-lft-identity_binary64_17623` `add-exp-log_binary64_17661` `pow1_binary64_17684`
8×	`sub-neg_binary64_17616` `associate-l/_binary64_17566` `associate-r/_binary64_17565` `distribute-lft-in_binary64_17572` `cancel-sign-sub-inv_binary64_17589` `distribute-rgt-in_binary64_17573`
4×	`*-commutative_binary64_17554` `prod-exp_binary64_17672` `unswap-sqr_binary64_17591` `cbrt-unprod_binary64_17656` `pow-prod-down_binary64_17694` `add-log-exp_binary64_17662`

Counts

4 → 120

Calls

4 calls:

11.0ms	(.f64 (-.f64 (.f64 x y2) (.f64 z y3)) (-.f64 (.f64 y0 c) (*.f64 y1 a)))
11.0ms	(.f64 (-.f64 (.f64 t j) (.f64 y k)) (-.f64 (.f64 y4 b) (*.f64 y5 i)))
11.0ms	(.f64 (-.f64 (.f64 k y2) (.f64 j y3)) (-.f64 (.f64 y4 y1) (*.f64 y5 y0)))
11.0ms	(.f64 (-.f64 (.f64 t y2) (.f64 y y3)) (-.f64 (.f64 y4 c) (*.f64 y5 a)))

series1.7s (4.1%)

Counts

4 → 12

Calls

4 calls:

444.0ms	(.f64 (-.f64 (.f64 k y2) (.f64 j y3)) (-.f64 (.f64 y4 y1) (*.f64 y5 y0)))
437.0ms	(.f64 (-.f64 (.f64 t j) (.f64 y k)) (-.f64 (.f64 y4 b) (*.f64 y5 i)))
436.0ms	(.f64 (-.f64 (.f64 t y2) (.f64 y y3)) (-.f64 (.f64 y4 c) (*.f64 y5 a)))
432.0ms	(.f64 (-.f64 (.f64 x y2) (.f64 z y3)) (-.f64 (.f64 y0 c) (*.f64 y1 a)))

simplify59.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	5041	4418

prune1.8s (4.3%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	113	19	132
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	114	19	133

Merged error: 18.9b

Counts

133 → 19

Compiler

Compiled 65477 to 31784 computations (51.5% saved)

localize69.0ms (0.2%)

Local error

Found 4 expressions with local error:

7.8b	(.f64 (-.f64 (.f64 x j) (.f64 z k)) (-.f64 (.f64 y0 b) (*.f64 y1 i)))
8.6b	(.f64 (-.f64 (.f64 x y2) (.f64 z y3)) (-.f64 (.f64 y0 c) (*.f64 y1 a)))
9.6b	(.f64 (-.f64 (.f64 t y2) (.f64 y y3)) (-.f64 (.f64 y4 c) (*.f64 y5 a)))
12.1b	(.f64 (-.f64 (.f64 k y2) (.f64 j y3)) (-.f64 (.f64 y4 y1) (*.f64 y5 y0)))

rewrite88.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`flip3--_binary64_17627` `flip--_binary64_17598`
20×	`add-sqr-sqrt_binary64_17645`
16×	`frac-times_binary64_17633`
12×	`add-cbrt-cube_binary64_17659` `associate-l_binary64_17564` `associate-r_binary64_17563` `add-cube-cbrt_binary64_17658` `*-un-lft-identity_binary64_17623` `add-exp-log_binary64_17661` `pow1_binary64_17684`
8×	`sub-neg_binary64_17616` `associate-l/_binary64_17566` `associate-r/_binary64_17565` `distribute-lft-in_binary64_17572` `cancel-sign-sub-inv_binary64_17589` `distribute-rgt-in_binary64_17573`
4×	`*-commutative_binary64_17554` `prod-exp_binary64_17672` `unswap-sqr_binary64_17591` `cbrt-unprod_binary64_17656` `pow-prod-down_binary64_17694` `add-log-exp_binary64_17662`

Counts

4 → 120

Calls

4 calls:

18.0ms	(.f64 (-.f64 (.f64 x y2) (.f64 z y3)) (-.f64 (.f64 y0 c) (*.f64 y1 a)))
12.0ms	(.f64 (-.f64 (.f64 x j) (.f64 z k)) (-.f64 (.f64 y0 b) (*.f64 y1 i)))
12.0ms	(.f64 (-.f64 (.f64 t y2) (.f64 y y3)) (-.f64 (.f64 y4 c) (*.f64 y5 a)))
11.0ms	(.f64 (-.f64 (.f64 k y2) (.f64 j y3)) (-.f64 (.f64 y4 y1) (*.f64 y5 y0)))

series1.7s (4%)

Counts

4 → 12

Calls

4 calls:

435.0ms	(.f64 (-.f64 (.f64 t y2) (.f64 y y3)) (-.f64 (.f64 y4 c) (*.f64 y5 a)))
433.0ms	(.f64 (-.f64 (.f64 x j) (.f64 z k)) (-.f64 (.f64 y0 b) (*.f64 y1 i)))
428.0ms	(.f64 (-.f64 (.f64 k y2) (.f64 j y3)) (-.f64 (.f64 y4 y1) (*.f64 y5 y0)))
420.0ms	(.f64 (-.f64 (.f64 x y2) (.f64 z y3)) (-.f64 (.f64 y0 c) (*.f64 y1 a)))

simplify56.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	5034	4424

prune1.1s (2.6%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	123	9	132
Fresh	1	17	18
Picked	1	0	1
Done	0	0	0
Total	125	26	151

Merged error: 17.8b

Counts

151 → 26

Compiler

Compiled 44193 to 18989 computations (57% saved)

localize76.0ms (0.2%)

Local error

Found 4 expressions with local error:

9.0b	(.f64 (-.f64 (.f64 j x) (.f64 k z)) (.f64 y0 b))
9.5b	(.f64 (-.f64 (.f64 j x) (.f64 k z)) (.f64 (neg.f64 y1) i))
9.6b	(.f64 (-.f64 (.f64 t y2) (.f64 y y3)) (-.f64 (.f64 y4 c) (*.f64 y5 a)))
12.1b	(.f64 (-.f64 (.f64 k y2) (.f64 j y3)) (-.f64 (.f64 y4 y1) (*.f64 y5 y0)))

rewrite78.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-cbrt-cube_binary64_17659` `add-exp-log_binary64_17661` `pow1_binary64_17684`
14×	`flip3--_binary64_17627` `add-sqr-sqrt_binary64_17645` `flip--_binary64_17598`
12×	`associate-l_binary64_17564`
10×	`add-cube-cbrt_binary64_17658` `*-un-lft-identity_binary64_17623`
8×	`prod-exp_binary64_17672` `frac-times_binary64_17633` `associate-r_binary64_17563` `cbrt-unprod_binary64_17656` `associate-*l/_binary64_17566` `pow-prod-down_binary64_17694`
4×	`-commutative_binary64_17554` `sub-neg_binary64_17616` `associate-r/_binary64_17565` `distribute-lft-in_binary64_17572` `add-log-exp_binary64_17662` `cancel-sign-sub-inv_binary64_17589` `distribute-rgt-in_binary64_17573`
2×	`unswap-sqr_binary64_17591`
1×	`distribute-lft-neg-out_binary64_17582` `distribute-rgt-neg-out_binary64_17583`

Counts

4 → 101

Calls

4 calls:

11.0ms	(.f64 (-.f64 (.f64 t y2) (.f64 y y3)) (-.f64 (.f64 y4 c) (*.f64 y5 a)))
11.0ms	(.f64 (-.f64 (.f64 k y2) (.f64 j y3)) (-.f64 (.f64 y4 y1) (*.f64 y5 y0)))
10.0ms	(.f64 (-.f64 (.f64 j x) (.f64 k z)) (.f64 (neg.f64 y1) i))
9.0ms	(.f64 (-.f64 (.f64 j x) (.f64 k z)) (.f64 y0 b))

series1.4s (3.2%)

Counts

4 → 12

Calls

4 calls:

439.0ms	(.f64 (-.f64 (.f64 t y2) (.f64 y y3)) (-.f64 (.f64 y4 c) (*.f64 y5 a)))
429.0ms	(.f64 (-.f64 (.f64 k y2) (.f64 j y3)) (-.f64 (.f64 y4 y1) (*.f64 y5 y0)))
256.0ms	(.f64 (-.f64 (.f64 j x) (.f64 k z)) (.f64 (neg.f64 y1) i))
237.0ms	(.f64 (-.f64 (.f64 j x) (.f64 k z)) (.f64 y0 b))

simplify63.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5383	3082

prune593.0ms (1.4%)

Pruning

27 alts after pruning (26 fresh and 1 done)

	Pruned	Kept	Total
New	110	3	113
Fresh	2	23	25
Picked	0	1	1
Done	0	0	0
Total	112	27	139

Merged error: 17.8b

Counts

139 → 27

Compiler

Compiled 24955 to 7865 computations (68.5% saved)

localize78.0ms (0.2%)

Local error

Found 4 expressions with local error:

8.8b	(cbrt.f64 (-.f64 (.f64 k y2) (.f64 j y3)))
8.8b	(cbrt.f64 (-.f64 (.f64 k y2) (.f64 j y3)))
8.8b	(cbrt.f64 (-.f64 (.f64 k y2) (.f64 j y3)))
9.6b	(.f64 (-.f64 (.f64 t y2) (.f64 y y3)) (-.f64 (.f64 y4 c) (*.f64 y5 a)))

rewrite46.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64_17645`
9×	`cbrt-prod_binary64_17654` `add-cube-cbrt_binary64_17658` `*-un-lft-identity_binary64_17623` `flip3--_binary64_17627` `flip--_binary64_17598`
6×	`add-cbrt-cube_binary64_17659` `cbrt-div_binary64_17655` `add-exp-log_binary64_17661` `pow1_binary64_17684`
4×	`frac-times_binary64_17633` `add-log-exp_binary64_17662`
3×	`associate-l_binary64_17564` `associate-r_binary64_17563` `pow1/3_binary64_17705`
2×	`sub-neg_binary64_17616` `associate-l/_binary64_17566` `associate-r/_binary64_17565` `distribute-lft-in_binary64_17572` `cancel-sign-sub-inv_binary64_17589` `distribute-rgt-in_binary64_17573`
1×	`*-commutative_binary64_17554` `prod-exp_binary64_17672` `unswap-sqr_binary64_17591` `cbrt-unprod_binary64_17656` `pow-prod-down_binary64_17694`

Counts

4 → 69

Calls

4 calls:

11.0ms	(.f64 (-.f64 (.f64 t y2) (.f64 y y3)) (-.f64 (.f64 y4 c) (*.f64 y5 a)))
4.0ms	(cbrt.f64 (-.f64 (.f64 k y2) (.f64 j y3)))
4.0ms	(cbrt.f64 (-.f64 (.f64 k y2) (.f64 j y3)))
4.0ms	(cbrt.f64 (-.f64 (.f64 k y2) (.f64 j y3)))

series1.3s (2.9%)

Counts

4 → 12

Calls

4 calls:

443.0ms	(.f64 (-.f64 (.f64 t y2) (.f64 y y3)) (-.f64 (.f64 y4 c) (*.f64 y5 a)))
275.0ms	(cbrt.f64 (-.f64 (.f64 k y2) (.f64 j y3)))
270.0ms	(cbrt.f64 (-.f64 (.f64 k y2) (.f64 j y3)))
268.0ms	(cbrt.f64 (-.f64 (.f64 k y2) (.f64 j y3)))

simplify47.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5219	2171

prune266.0ms (0.6%)

Pruning

27 alts after pruning (25 fresh and 2 done)

	Pruned	Kept	Total
New	81	0	81
Fresh	0	25	25
Picked	0	1	1
Done	0	1	1
Total	81	27	108

Merged error: 17.8b

Counts

108 → 27

Compiler

Compiled 13505 to 2385 computations (82.3% saved)

regimes2.5s (5.9%)

Compiler: Compiled 45216 to 28704 computations (36.5% saved)

bsearch1.9s (4.4%)

Steps

Iters	Range		Point
10	2.518546726810263e+19	2.8768161505073052e+29	1.6993593057573185e+28
10	2.716824283988483e-125	8.174620122822222e-112	3.799220561055938e-115
8	4.813312795203643e-236	2.2919410966885977e-232	2.2535741933984323e-232
8	-5.478052435062931e-244	-2.108798713751737e-247	-2.084771845020372e-244
6	-2.4342514532541205e-177	-4.1420495227673484e-178	-4.782303445049792e-178

Compiler

Compiled 1 to 16 computations (-1500% saved)

simplify48.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	1131	987
1	1131	987

end0.0ms (0%)

sample21.9s (51.2%)

Algorithm

1×

intervals

Results

12.8s	64568×	body	128	invalid
1.6s	8000×	body	128	valid

Compiler

Compiled 4284 to 2134 computations (50.2% saved)

Details

analyze4.8s (11.3%)

sample654.0ms (1.5%)

simplify210.0ms (0.5%)

prune6.0ms (0%)

localize67.0ms (0.2%)

rewrite84.0ms (0.2%)

series1.7s (4.1%)

simplify59.0ms (0.1%)

prune1.8s (4.3%)

localize69.0ms (0.2%)

rewrite88.0ms (0.2%)

series1.7s (4%)

simplify56.0ms (0.1%)

prune1.1s (2.6%)

localize76.0ms (0.2%)

rewrite78.0ms (0.2%)

series1.4s (3.2%)

simplify63.0ms (0.1%)

prune593.0ms (1.4%)

localize78.0ms (0.2%)

rewrite46.0ms (0.1%)

series1.3s (2.9%)

simplify47.0ms (0.1%)

prune266.0ms (0.6%)

regimes2.5s (5.9%)

bsearch1.9s (4.4%)

simplify48.0ms (0.1%)

end0.0ms (0%)

sample21.9s (51.2%)

Profiling