Details

analyze5.6s (11.4%)

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)

sample676.0ms (1.4%)

Algorithm

1×

intervals

Results

423.0ms	1758×	body	80	invalid
61.0ms	256×	body	80	valid

Compiler

Compiled 191 to 143 computations (25.1% saved)

simplify57.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5429	142

prune20.0ms (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: 28.8b

Counts

2 → 1

Compiler

Compiled 190 to 126 computations (33.7% saved)

localize69.0ms (0.1%)

Local error

Found 4 expressions with local error:

8.7b	(.f64 (-.f64 (.f64 t j) (.f64 y k)) (-.f64 (.f64 y4 b) (*.f64 y5 i)))
9.0b	(.f64 (-.f64 (.f64 k y2) (.f64 j y3)) (-.f64 (.f64 y4 y1) (*.f64 y5 y0)))
9.7b	(.f64 (-.f64 (.f64 x j) (.f64 z k)) (-.f64 (.f64 y0 b) (*.f64 y1 i)))
10.9b	(.f64 (-.f64 (.f64 x y2) (.f64 z y3)) (-.f64 (.f64 y0 c) (*.f64 y1 a)))

rewrite46.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`flip3--_binary64` `flip--_binary64`
20×	`add-sqr-sqrt_binary64`
16×	`frac-times_binary64`
12×	`-un-lft-identity_binary64` `pow1_binary64` `associate-r_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-l*_binary64`
8×	`sub-neg_binary64` `associate-r/_binary64` `associate-l/_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

4 → 112

Calls

4 calls:

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

series259.0ms (0.5%)

Counts

4 → 12

Calls

4 calls:

71.0ms	(.f64 (-.f64 (.f64 x j) (.f64 z k)) (-.f64 (.f64 y0 b) (*.f64 y1 i)))
65.0ms	(.f64 (-.f64 (.f64 x y2) (.f64 z y3)) (-.f64 (.f64 y0 c) (*.f64 y1 a)))
64.0ms	(.f64 (-.f64 (.f64 t j) (.f64 y k)) (-.f64 (.f64 y4 b) (*.f64 y5 i)))
58.0ms	(.f64 (-.f64 (.f64 k y2) (.f64 j y3)) (-.f64 (.f64 y4 y1) (*.f64 y5 y0)))

simplify98.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5043	4158

prune358.0ms (0.7%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	105	19	124
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	106	19	125

Merged error: 21.1b

Counts

125 → 19

Compiler

Compiled 15450 to 2183 computations (85.9% saved)

localize69.0ms (0.1%)

Local error

Found 4 expressions with local error:

9.0b	(.f64 (-.f64 (.f64 k y2) (.f64 j y3)) (-.f64 (.f64 y4 y1) (*.f64 y5 y0)))
9.0b	(.f64 (-.f64 (.f64 x j) (.f64 z k)) (.f64 y0 b))
10.1b	(.f64 (-.f64 (.f64 x j) (.f64 z k)) (neg.f64 (.f64 y1 i)))
10.9b	(.f64 (-.f64 (.f64 x y2) (.f64 z y3)) (-.f64 (.f64 y0 c) (*.f64 y1 a)))

rewrite47.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
15×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`flip3--_binary64` `flip--_binary64`
13×	`associate-r_binary64`
12×	`associate-l_binary64`
11×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
8×	`frac-times_binary64` `associate-*l/_binary64`
6×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
4×	`add-log-exp_binary64` `sub-neg_binary64` `associate-r/_binary64` `-commutative_binary64`
3×	`unswap-sqr_binary64`
2×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
1×	`distribute-rgt-neg-out_binary64` `neg-mul-1_binary64` `distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64`

Counts

4 → 100

Calls

4 calls:

13.0ms	(.f64 (-.f64 (.f64 x y2) (.f64 z y3)) (-.f64 (.f64 y0 c) (*.f64 y1 a)))
12.0ms	(.f64 (-.f64 (.f64 k y2) (.f64 j y3)) (-.f64 (.f64 y4 y1) (*.f64 y5 y0)))
10.0ms	(.f64 (-.f64 (.f64 x j) (.f64 z k)) (.f64 y0 b))
9.0ms	(.f64 (-.f64 (.f64 x j) (.f64 z k)) (neg.f64 (.f64 y1 i)))

series191.0ms (0.4%)

Counts

4 → 12

Calls

4 calls:

60.0ms	(.f64 (-.f64 (.f64 x y2) (.f64 z y3)) (-.f64 (.f64 y0 c) (*.f64 y1 a)))
59.0ms	(.f64 (-.f64 (.f64 k y2) (.f64 j y3)) (-.f64 (.f64 y4 y1) (*.f64 y5 y0)))
39.0ms	(.f64 (-.f64 (.f64 x j) (.f64 z k)) (neg.f64 (.f64 y1 i)))
33.0ms	(.f64 (-.f64 (.f64 x j) (.f64 z k)) (.f64 y0 b))

simplify114.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4986	3016
1	4986	3016

prune303.0ms (0.6%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	110	2	112
Fresh	1	17	18
Picked	1	0	1
Done	0	0	0
Total	112	19	131

Merged error: 20.3b

Counts

131 → 19

Compiler

Compiled 14754 to 2071 computations (86% saved)

localize74.0ms (0.2%)

Local error

Found 4 expressions with local error:

8.2b	(.f64 (-.f64 (.f64 t y2) (.f64 y y3)) (-.f64 (.f64 y4 c) (*.f64 y5 a)))
8.7b	(.f64 (-.f64 (.f64 t j) (.f64 y k)) (-.f64 (.f64 y4 b) (*.f64 y5 i)))
9.0b	(.f64 (-.f64 (.f64 k y2) (.f64 j y3)) (-.f64 (.f64 y4 y1) (*.f64 y5 y0)))
9.7b	(.f64 (-.f64 (.f64 x j) (.f64 z k)) (-.f64 (.f64 y0 b) (*.f64 y1 i)))

rewrite46.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`flip3--_binary64` `flip--_binary64`
20×	`add-sqr-sqrt_binary64`
16×	`frac-times_binary64`
12×	`-un-lft-identity_binary64` `pow1_binary64` `associate-r_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-l*_binary64`
8×	`sub-neg_binary64` `associate-r/_binary64` `associate-l/_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

4 → 112

Calls

4 calls:

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

series223.0ms (0.5%)

Counts

4 → 12

Calls

4 calls:

58.0ms	(.f64 (-.f64 (.f64 x j) (.f64 z k)) (-.f64 (.f64 y0 b) (*.f64 y1 i)))
56.0ms	(.f64 (-.f64 (.f64 t y2) (.f64 y y3)) (-.f64 (.f64 y4 c) (*.f64 y5 a)))
55.0ms	(.f64 (-.f64 (.f64 k y2) (.f64 j y3)) (-.f64 (.f64 y4 y1) (*.f64 y5 y0)))
54.0ms	(.f64 (-.f64 (.f64 t j) (.f64 y k)) (-.f64 (.f64 y4 b) (*.f64 y5 i)))

simplify87.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5041	4158

prune315.0ms (0.6%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	118	6	124
Fresh	1	17	18
Picked	1	0	1
Done	0	0	0
Total	120	23	143

Merged error: 19.3b

Counts

143 → 23

Compiler

Compiled 18316 to 2412 computations (86.8% saved)

localize74.0ms (0.2%)

Local error

Found 4 expressions with local error:

8.7b	(cbrt.f64 (-.f64 (.f64 y0 c) (.f64 y1 a)))
8.7b	(cbrt.f64 (-.f64 (.f64 y0 c) (.f64 y1 a)))
9.0b	(.f64 (-.f64 (.f64 k y2) (.f64 j y3)) (-.f64 (.f64 y4 y1) (*.f64 y5 y0)))
9.7b	(.f64 (-.f64 (.f64 x j) (.f64 z k)) (-.f64 (.f64 y0 b) (*.f64 y1 i)))

rewrite32.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`flip3--_binary64` `add-sqr-sqrt_binary64` `flip--_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
8×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `frac-times_binary64`
6×	`associate-r_binary64` `associate-l_binary64` `cbrt-prod_binary64`
4×	`cbrt-div_binary64` `add-log-exp_binary64` `sub-neg_binary64` `associate-r/_binary64` `associate-l/_binary64`
2×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `pow1/3_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

4 → 82

Calls

4 calls:

11.0ms	(.f64 (-.f64 (.f64 x j) (.f64 z k)) (-.f64 (.f64 y0 b) (*.f64 y1 i)))
10.0ms	(.f64 (-.f64 (.f64 k y2) (.f64 j y3)) (-.f64 (.f64 y4 y1) (*.f64 y5 y0)))
4.0ms	(cbrt.f64 (-.f64 (.f64 y0 c) (.f64 y1 a)))
4.0ms	(cbrt.f64 (-.f64 (.f64 y0 c) (.f64 y1 a)))

series197.0ms (0.4%)

Counts

4 → 12

Calls

4 calls:

61.0ms	(.f64 (-.f64 (.f64 x j) (.f64 z k)) (-.f64 (.f64 y0 b) (*.f64 y1 i)))
57.0ms	(.f64 (-.f64 (.f64 k y2) (.f64 j y3)) (-.f64 (.f64 y4 y1) (*.f64 y5 y0)))
40.0ms	(cbrt.f64 (-.f64 (.f64 y0 c) (.f64 y1 a)))
39.0ms	(cbrt.f64 (-.f64 (.f64 y0 c) (.f64 y1 a)))

simplify76.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5038	2780

prune123.0ms (0.2%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	91	3	94
Fresh	1	21	22
Picked	1	0	1
Done	0	0	0
Total	93	24	117

Merged error: 18.9b

Counts

117 → 24

Compiler

Compiled 11826 to 785 computations (93.4% saved)

regimes5.8s (11.7%)

Compiler: Compiled 43056 to 26128 computations (39.3% saved)

bsearch1.9s (3.8%)

Steps

Iters	Range		Point
10	8.530252929843237e-51	1.1750268074105762e-34	7.283977372420719e-43
6	-8.130127454213013e-176	-9.539830181663899e-177	-5.324316910037147e-176
10	-1.1518731467569447e-99	-1.9916392792192013e-109	-2.057285223741706e-108
8	-641618937783.4966	-14013081.716683488	-1524701509.710893

Compiler

Compiled 1 to 16 computations (-1500% saved)

simplify125.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (113.0ms)

Iter	Nodes	Cost
0	2159	758
1	2159	758

end0.0ms (0%)

sample32.5s (65.7%)

Algorithm

1×

intervals

Results

16.8s	64513×	body	80	invalid
2.1s	8000×	body	80	valid

Compiler

Compiled 3999 to 1972 computations (50.7% saved)

Details

analyze5.6s (11.4%)

sample676.0ms (1.4%)

simplify57.0ms (0.1%)

prune20.0ms (0%)

localize69.0ms (0.1%)

rewrite46.0ms (0.1%)

series259.0ms (0.5%)

simplify98.0ms (0.2%)

prune358.0ms (0.7%)

localize69.0ms (0.1%)

rewrite47.0ms (0.1%)

series191.0ms (0.4%)

simplify114.0ms (0.2%)

prune303.0ms (0.6%)

localize74.0ms (0.2%)

rewrite46.0ms (0.1%)

series223.0ms (0.5%)

simplify87.0ms (0.2%)

prune315.0ms (0.6%)

localize74.0ms (0.2%)

rewrite32.0ms (0.1%)

series197.0ms (0.4%)

simplify76.0ms (0.2%)

prune123.0ms (0.2%)

regimes5.8s (11.7%)

bsearch1.9s (3.8%)

simplify125.0ms (0.3%)

end0.0ms (0%)

sample32.5s (65.7%)

Profiling