Details

analyze511.0ms (12.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
6.2%	93.6%	0.2%	8
25%	74.9%	0.2%	9
28.1%	71.7%	0.2%	10
29.6%	70.2%	0.2%	11
53%	46.8%	0.2%	12
71.3%	28.5%	0.2%	13
71.7%	28.1%	0.2%	14

Compiler

Compiled 16 to 12 computations (25% saved)

sample20.0ms (0.5%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
1.0ms	15×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify223.0ms (5.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (128.0ms)

Iter	Nodes	Cost
0	5230	22

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: 27.9b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize14.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 c c) (.f64 d d))
0.2b	(-.f64 (.f64 b c) (.f64 a d))
27.4b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d)))

rewrite20.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64_3147` `add-sqr-sqrt_binary64_3169` `add-cube-cbrt_binary64_3182`
9×	`times-frac_binary64_3153`
7×	`add-log-exp_binary64_3186`
5×	`add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183`
3×	`associate-/r_binary64_3091` `pow1_binary64_3208` `associate-/l_binary64_3092`
2×	`flip--_binary64_3122` `flip-+_binary64_3121` `flip3--_binary64_3151` `flip3-+_binary64_3150` `associate-/l/_binary64_3094` `associate-/r/_binary64_3093`
1×	`clear-num_binary64_3146` `cancel-sign-sub-inv_binary64_3113` `frac-2neg_binary64_3158` `sub-neg_binary64_3140` `+-commutative_binary64_3077` `div-sub_binary64_3152` `cbrt-undiv_binary64_3181` `div-exp_binary64_3198` `diff-log_binary64_3239` `div-inv_binary64_3144` `sum-log_binary64_3238`

Counts

3 → 55

Calls

3 calls:

8.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(+.f64 (.f64 c c) (.f64 d d))
3.0ms	(-.f64 (.f64 b c) (.f64 a d))

series163.0ms (3.9%)

Counts

3 → 9

Calls

3 calls:

100.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d)))
41.0ms	(-.f64 (.f64 b c) (.f64 a d))
23.0ms	(+.f64 (.f64 c c) (.f64 d d))

simplify83.0ms (2%)

Algorithm

1×	egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4935	1462
1	4935	1462

prune74.0ms (1.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	56	8	64
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	56	9	65

Merged error: 27.2b

Counts

65 → 9

Compiler

Compiled 1655 to 306 computations (81.5% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(-.f64 (.f64 b c) (.f64 a d))
14.7b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
30.8b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
30.8b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite31.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64_3169`
21×	`*-un-lft-identity_binary64_3147` `add-cube-cbrt_binary64_3182`
18×	`times-frac_binary64_3153` `sqrt-prod_binary64_3163`
6×	`add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183` `associate-/r*_binary64_3091` `pow1_binary64_3208` `add-log-exp_binary64_3186` `sqrt-div_binary64_3164`
3×	`flip-+_binary64_3121` `flip3-+_binary64_3150` `associate-/l*_binary64_3092`
2×	`flip--_binary64_3122` `flip3--_binary64_3151` `associate-/l/_binary64_3094` `rem-sqrt-square_binary64_3160` `sqrt-pow1_binary64_3165` `pow1/2_binary64_3227` `associate-/r/_binary64_3093`
1×	`clear-num_binary64_3146` `cancel-sign-sub-inv_binary64_3113` `frac-2neg_binary64_3158` `sub-neg_binary64_3140` `div-sub_binary64_3152` `cbrt-undiv_binary64_3181` `div-exp_binary64_3198` `diff-log_binary64_3239` `div-inv_binary64_3144`

Counts

4 → 86

Calls

4 calls:

9.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(-.f64 (.f64 b c) (.f64 a d))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

series227.0ms (5.5%)

Counts

4 → 12

Calls

4 calls:

130.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
47.0ms	(-.f64 (.f64 b c) (.f64 a d))
25.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
25.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

simplify69.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5136	2374

prune98.0ms (2.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	93	5	98
Fresh	3	4	7
Picked	0	1	1
Done	1	0	1
Total	97	10	107

Merged error: 24.2b

Counts

107 → 10

Compiler

Compiled 3420 to 479 computations (86% saved)

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.2b	(-.f64 (.f64 c b) (.f64 d a))
14.8b	(/.f64 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))) (-.f64 (.f64 c b) (.f64 d a)))
30.8b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
30.8b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite29.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64_3169`
21×	`*-un-lft-identity_binary64_3147` `add-cube-cbrt_binary64_3182`
18×	`times-frac_binary64_3153` `sqrt-prod_binary64_3163`
6×	`add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183` `pow1_binary64_3208` `add-log-exp_binary64_3186` `associate-/l*_binary64_3092` `sqrt-div_binary64_3164`
3×	`flip-+_binary64_3121` `associate-/r*_binary64_3091` `flip3-+_binary64_3150`
2×	`flip--_binary64_3122` `flip3--_binary64_3151` `associate-/l/_binary64_3094` `rem-sqrt-square_binary64_3160` `sqrt-pow1_binary64_3165` `pow1/2_binary64_3227` `associate-/r/_binary64_3093`
1×	`clear-num_binary64_3146` `cancel-sign-sub-inv_binary64_3113` `frac-2neg_binary64_3158` `sub-neg_binary64_3140` `cbrt-undiv_binary64_3181` `div-exp_binary64_3198` `diff-log_binary64_3239` `div-inv_binary64_3144`

Counts

4 → 85

Calls

4 calls:

9.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))) (-.f64 (.f64 c b) (.f64 d a)))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(-.f64 (.f64 c b) (.f64 d a))

series177.0ms (4.3%)

Counts

4 → 12

Calls

4 calls:

91.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))) (-.f64 (.f64 c b) (.f64 d a)))
38.0ms	(-.f64 (.f64 c b) (.f64 d a))
24.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
23.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

simplify66.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5105	2358

prune98.0ms (2.4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	97	10	107

Merged error: 24.2b

Counts

107 → 10

Compiler

Compiled 3571 to 667 computations (81.3% saved)

localize42.0ms (1%)

Local error

Found 4 expressions with local error:

12.8b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 (.f64 c c) (.f64 d d))) (cbrt.f64 (+.f64 (.f64 c c) (.f64 d d))))) (/.f64 (-.f64 (.f64 b c) (.f64 a d)) (cbrt.f64 (+.f64 (.f64 c c) (.f64 d d)))))
31.8b	(cbrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
31.8b	(cbrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
31.8b	(cbrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite73.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

49×	`add-exp-log_binary64_3185`
43×	`add-sqr-sqrt_binary64_3169`
33×	`times-frac_binary64_3153`
25×	`*-un-lft-identity_binary64_3147`
24×	`associate-r_binary64_3087`
22×	`add-cube-cbrt_binary64_3182`
21×	`cbrt-prod_binary64_3178`
20×	`cbrt-div_binary64_3179` `prod-exp_binary64_3196`
18×	`add-cbrt-cube_binary64_3183`
15×	`div-exp_binary64_3198` `associate-l_binary64_3088`
10×	`flip-+_binary64_3121` `flip3-+_binary64_3150` `associate-/r/_binary64_3093`
9×	`unswap-sqr_binary64_3115`
8×	`cbrt-unprod_binary64_3180`
7×	`cbrt-undiv_binary64_3181`
6×	`pow1_binary64_3208`
5×	`frac-times_binary64_3157`
4×	`add-log-exp_binary64_3186` `1-exp_binary64_3191` `rec-exp_binary64_3197`
3×	`pow1/3_binary64_3229` `associate-l/_binary64_3090` `associate-r/_binary64_3089`
2×	`div-inv_binary64_3144`
1×	`*-commutative_binary64_3078` `pow-prod-down_binary64_3218`

Counts

4 → 119

Calls

4 calls:

34.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 (.f64 c c) (.f64 d d))) (cbrt.f64 (+.f64 (.f64 c c) (.f64 d d))))) (/.f64 (-.f64 (.f64 b c) (.f64 a d)) (cbrt.f64 (+.f64 (.f64 c c) (.f64 d d)))))
7.0ms	(cbrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
7.0ms	(cbrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
7.0ms	(cbrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

series375.0ms (9%)

Counts

4 → 12

Calls

4 calls:

143.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 (.f64 c c) (.f64 d d))) (cbrt.f64 (+.f64 (.f64 c c) (.f64 d d))))) (/.f64 (-.f64 (.f64 b c) (.f64 a d)) (cbrt.f64 (+.f64 (.f64 c c) (.f64 d d)))))
85.0ms	(cbrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
76.0ms	(cbrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
71.0ms	(cbrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

simplify100.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4954	4576
1	4954	4576

prune133.0ms (3.2%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	131	10	141

Merged error: 24.2b

Counts

141 → 10

Compiler

Compiled 5391 to 733 computations (86.4% saved)

regimes332.0ms (8%)

Compiler: Compiled 4585 to 2438 computations (46.8% saved)

bsearch23.0ms (0.6%)

Steps

Iters	Range		Point
8	-4.531592128318667e+131	-3.199838483210276e+128	-2.531747356501993e+130

Compiler

Compiled 1 to 4 computations (-300% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	69	75
1	69	75

end0.0ms (0%)

sample1.1s (27.3%)

Algorithm

1×

intervals

Results

340.0ms	8000×	body	128	valid
22.0ms	468×	body	128	invalid

Compiler

Compiled 982 to 517 computations (47.4% saved)

Details

analyze511.0ms (12.3%)

sample20.0ms (0.5%)

simplify223.0ms (5.4%)

prune2.0ms (0.1%)

localize14.0ms (0.3%)

rewrite20.0ms (0.5%)

series163.0ms (3.9%)

simplify83.0ms (2%)

prune74.0ms (1.8%)

localize12.0ms (0.3%)

rewrite31.0ms (0.8%)

series227.0ms (5.5%)

simplify69.0ms (1.7%)

prune98.0ms (2.4%)

localize16.0ms (0.4%)

rewrite29.0ms (0.7%)

series177.0ms (4.3%)

simplify66.0ms (1.6%)

prune98.0ms (2.4%)

localize42.0ms (1%)

rewrite73.0ms (1.8%)

series375.0ms (9%)

simplify100.0ms (2.4%)

prune133.0ms (3.2%)

regimes332.0ms (8%)

bsearch23.0ms (0.6%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.1s (27.3%)

Profiling