Details

analyze526.0ms (12.8%)

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)

sample23.0ms (0.6%)

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)

simplify218.0ms (5.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (120.0ms)

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: 22.1b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 c c) (.f64 d d))
0.5b	(-.f64 (.f64 b c) (.f64 a d))
21.6b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d)))

rewrite21.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64_2828` `*-un-lft-identity_binary64_2806` `add-cube-cbrt_binary64_2841`
9×	`times-frac_binary64_2812`
7×	`add-log-exp_binary64_2845`
5×	`add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842`
3×	`associate-/r_binary64_2750` `associate-/l_binary64_2751` `pow1_binary64_2867`
2×	`associate-/l/_binary64_2753` `flip3--_binary64_2810` `flip-+_binary64_2780` `flip--_binary64_2781` `flip3-+_binary64_2809` `associate-/r/_binary64_2752`
1×	`cancel-sign-sub-inv_binary64_2772` `div-inv_binary64_2803` `div-exp_binary64_2857` `cbrt-undiv_binary64_2840` `div-sub_binary64_2811` `diff-log_binary64_2898` `sub-neg_binary64_2799` `sum-log_binary64_2897` `clear-num_binary64_2805` `frac-2neg_binary64_2817` `+-commutative_binary64_2736`

Counts

3 → 55

Calls

3 calls:

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

series167.0ms (4.1%)

Counts

3 → 9

Calls

3 calls:

104.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d)))
42.0ms	(-.f64 (.f64 b c) (.f64 a d))
21.0ms	(+.f64 (.f64 c c) (.f64 d d))

simplify85.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4935	1462
1	4935	1462

prune77.0ms (1.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	55	9	64
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	55	10	65

Merged error: 21.5b

Counts

65 → 10

Compiler

Compiled 1709 to 319 computations (81.3% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(-.f64 (.f64 b c) (.f64 a d))
11.6b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
25.8b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
25.8b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite29.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64_2828`
21×	`*-un-lft-identity_binary64_2806` `add-cube-cbrt_binary64_2841`
18×	`times-frac_binary64_2812` `sqrt-prod_binary64_2822`
6×	`sqrt-div_binary64_2823` `add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842` `associate-/r*_binary64_2750` `add-log-exp_binary64_2845` `pow1_binary64_2867`
3×	`flip-+_binary64_2780` `flip3-+_binary64_2809` `associate-/l*_binary64_2751`
2×	`associate-/l/_binary64_2753` `pow1/2_binary64_2886` `flip3--_binary64_2810` `sqrt-pow1_binary64_2824` `rem-sqrt-square_binary64_2819` `flip--_binary64_2781` `associate-/r/_binary64_2752`
1×	`cancel-sign-sub-inv_binary64_2772` `div-inv_binary64_2803` `div-exp_binary64_2857` `cbrt-undiv_binary64_2840` `div-sub_binary64_2811` `diff-log_binary64_2898` `sub-neg_binary64_2799` `clear-num_binary64_2805` `frac-2neg_binary64_2817`

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

series215.0ms (5.2%)

Counts

4 → 12

Calls

4 calls:

122.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
40.0ms	(-.f64 (.f64 b c) (.f64 a d))
27.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
26.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

simplify68.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5136	2374

prune107.0ms (2.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	91	7	98
Fresh	4	4	8
Picked	1	0	1
Done	0	1	1
Total	96	12	108

Merged error: 19.0b

Counts

108 → 12

Compiler

Compiled 3474 to 507 computations (85.4% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(-.f64 (.f64 c b) (.f64 d a))
11.7b	(/.f64 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))) (-.f64 (.f64 c b) (.f64 d a)))
25.8b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
25.8b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite31.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64_2828`
21×	`*-un-lft-identity_binary64_2806` `add-cube-cbrt_binary64_2841`
18×	`times-frac_binary64_2812` `sqrt-prod_binary64_2822`
6×	`sqrt-div_binary64_2823` `add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842` `add-log-exp_binary64_2845` `associate-/l*_binary64_2751` `pow1_binary64_2867`
3×	`associate-/r*_binary64_2750` `flip-+_binary64_2780` `flip3-+_binary64_2809`
2×	`associate-/l/_binary64_2753` `pow1/2_binary64_2886` `flip3--_binary64_2810` `sqrt-pow1_binary64_2824` `rem-sqrt-square_binary64_2819` `flip--_binary64_2781` `associate-/r/_binary64_2752`
1×	`cancel-sign-sub-inv_binary64_2772` `div-inv_binary64_2803` `div-exp_binary64_2857` `cbrt-undiv_binary64_2840` `diff-log_binary64_2898` `sub-neg_binary64_2799` `clear-num_binary64_2805` `frac-2neg_binary64_2817`

Counts

4 → 85

Calls

4 calls:

12.0ms	(/.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	(-.f64 (.f64 c b) (.f64 d a))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

series176.0ms (4.3%)

Counts

4 → 12

Calls

4 calls:

81.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))) (-.f64 (.f64 c b) (.f64 d a)))
47.0ms	(-.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)))

simplify64.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5105	2358

prune104.0ms (2.5%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	97	12	109

Merged error: 19.0b

Counts

109 → 12

Compiler

Compiled 3625 to 695 computations (80.8% saved)

localize17.0ms (0.4%)

Local error

Found 4 expressions with local error:

12.3b	(cbrt.f64 (-.f64 (.f64 b c) (.f64 a d)))
12.3b	(cbrt.f64 (-.f64 (.f64 b c) (.f64 a d)))
25.8b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
25.8b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite23.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_2828`
8×	`*-un-lft-identity_binary64_2806` `add-cube-cbrt_binary64_2841`
6×	`sqrt-prod_binary64_2822` `cbrt-prod_binary64_2837` `pow1_binary64_2867`
4×	`sqrt-div_binary64_2823` `cbrt-div_binary64_2838` `add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842` `add-log-exp_binary64_2845`
2×	`pow1/2_binary64_2886` `pow1/3_binary64_2888` `flip3--_binary64_2810` `sqrt-pow1_binary64_2824` `rem-sqrt-square_binary64_2819` `flip-+_binary64_2780` `flip--_binary64_2781` `flip3-+_binary64_2809`

Counts

4 → 56

Calls

4 calls:

6.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(cbrt.f64 (-.f64 (.f64 b c) (.f64 a d)))
3.0ms	(cbrt.f64 (-.f64 (.f64 b c) (.f64 a d)))

series344.0ms (8.4%)

Counts

4 → 12

Calls

4 calls:

148.0ms	(cbrt.f64 (-.f64 (.f64 b c) (.f64 a d)))
148.0ms	(cbrt.f64 (-.f64 (.f64 b c) (.f64 a d)))
24.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
23.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

simplify125.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (108.0ms)

Iter	Nodes	Cost
0	4855	1130
1	4855	1130

prune79.0ms (1.9%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	67	13	80

Merged error: 19.0b

Counts

80 → 13

Compiler

Compiled 3376 to 338 computations (90% saved)

regimes356.0ms (8.7%)

Compiler: Compiled 4727 to 2611 computations (44.8% saved)

bsearch2.0ms (0%)

Compiler: Compiled 15 to 11 computations (26.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	56	82
1	56	82

end0.0ms (0%)

sample1.2s (29.3%)

Algorithm

1×

intervals

Results

337.0ms	8000×	body	128	valid
18.0ms	450×	body	128	invalid

Compiler

Compiled 1012 to 549 computations (45.8% saved)

Details

analyze526.0ms (12.8%)

sample23.0ms (0.6%)

simplify218.0ms (5.3%)

prune2.0ms (0.1%)

localize10.0ms (0.2%)

rewrite21.0ms (0.5%)

series167.0ms (4.1%)

simplify85.0ms (2.1%)

prune77.0ms (1.9%)

localize13.0ms (0.3%)

rewrite29.0ms (0.7%)

series215.0ms (5.2%)

simplify68.0ms (1.6%)

prune107.0ms (2.6%)

localize14.0ms (0.3%)

rewrite31.0ms (0.8%)

series176.0ms (4.3%)

simplify64.0ms (1.6%)

prune104.0ms (2.5%)

localize17.0ms (0.4%)

rewrite23.0ms (0.6%)

series344.0ms (8.4%)

simplify125.0ms (3.1%)

prune79.0ms (1.9%)

regimes356.0ms (8.7%)

bsearch2.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.2s (29.3%)

Profiling