Details

analyze728.0ms (11.9%)

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)

sample24.0ms (0.4%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
1.0ms	16×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify166.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	16	22
1	16	22

prune2.0ms (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: 27.2b

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))
0.9b	(+.f64 (.f64 a c) (.f64 b d))
26.7b	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))

rewrite25.0ms (0.4%)

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`
4×	`flip-+_binary64_3121` `flip3-+_binary64_3150`
3×	`associate-/r_binary64_3091` `pow1_binary64_3208` `associate-/l_binary64_3092`
2×	`associate-/l/_binary64_3094` `+-commutative_binary64_3077` `associate-/r/_binary64_3093` `sum-log_binary64_3238`
1×	`clear-num_binary64_3146` `frac-2neg_binary64_3158` `cbrt-undiv_binary64_3181` `div-exp_binary64_3198` `div-inv_binary64_3144`

Counts

3 → 53

Calls

3 calls:

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

series307.0ms (5%)

Counts

3 → 9

Calls

3 calls:

181.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))
83.0ms	(+.f64 (.f64 a c) (.f64 b d))
43.0ms	(+.f64 (.f64 c c) (.f64 d d))

simplify44.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5006	1420

prune77.0ms (1.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	55	7	62
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	55	8	63

Merged error: 26.4b

Counts

63 → 8

Compiler

Compiled 1626 to 287 computations (82.3% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.9b	(+.f64 (.f64 a c) (.f64 b d))
16.8b	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
30.2b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
30.2b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite33.0ms (0.5%)

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`
5×	`flip-+_binary64_3121` `flip3-+_binary64_3150`
3×	`associate-/l*_binary64_3092`
2×	`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` `frac-2neg_binary64_3158` `+-commutative_binary64_3077` `cbrt-undiv_binary64_3181` `div-exp_binary64_3198` `div-inv_binary64_3144` `sum-log_binary64_3238`

Counts

4 → 84

Calls

4 calls:

10.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
5.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
5.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(+.f64 (.f64 a c) (.f64 b d))

series410.0ms (6.7%)

Counts

4 → 12

Calls

4 calls:

240.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
75.0ms	(+.f64 (.f64 a c) (.f64 b d))
50.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
45.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

simplify66.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5228	2326

prune97.0ms (1.6%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	90	6	96
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	92	12	104

Merged error: 24.2b

Counts

104 → 12

Compiler

Compiled 3342 to 478 computations (85.7% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

8.9b	(cbrt.f64 (/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d))))
26.7b	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))
26.7b	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))
26.7b	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))

rewrite57.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`times-frac_binary64_3153`
35×	`*-un-lft-identity_binary64_3147` `add-sqr-sqrt_binary64_3169` `add-cube-cbrt_binary64_3182`
15×	`cbrt-prod_binary64_3178`
10×	`add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183`
9×	`associate-/r_binary64_3091` `associate-/l_binary64_3092`
8×	`associate-/r/_binary64_3093`
7×	`flip-+_binary64_3121` `flip3-+_binary64_3150`
6×	`associate-/l/_binary64_3094`
4×	`pow1_binary64_3208` `add-log-exp_binary64_3186` `div-inv_binary64_3144`
3×	`clear-num_binary64_3146` `frac-2neg_binary64_3158` `cbrt-undiv_binary64_3181` `div-exp_binary64_3198`
1×	`cbrt-div_binary64_3179` `pow1/3_binary64_3229`

Counts

4 → 117

Calls

4 calls:

10.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))
10.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))
9.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))
7.0ms	(cbrt.f64 (/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d))))

series944.0ms (15.5%)

Counts

4 → 12

Calls

4 calls:

426.0ms	(cbrt.f64 (/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d))))
178.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))
176.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))
164.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))

simplify97.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5026	4022

prune169.0ms (2.8%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	128	1	129
Fresh	1	8	9
Picked	0	1	1
Done	0	2	2
Total	129	12	141

Merged error: 24.2b

Counts

141 → 12

Compiler

Compiled 7913 to 687 computations (91.3% saved)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

10.2b	(pow.f64 (/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d))) 1/3)
26.7b	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))
26.7b	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))
26.7b	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))

rewrite60.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`times-frac_binary64_3153` `*-un-lft-identity_binary64_3147` `add-sqr-sqrt_binary64_3169` `add-cube-cbrt_binary64_3182`
15×	`unpow-prod-down_binary64_3226`
13×	`add-exp-log_binary64_3185`
10×	`add-cbrt-cube_binary64_3183`
9×	`associate-/r_binary64_3091` `associate-/l_binary64_3092`
8×	`associate-/r/_binary64_3093`
7×	`flip-+_binary64_3121` `flip3-+_binary64_3150`
6×	`associate-/l/_binary64_3094`
5×	`pow1_binary64_3208`
4×	`div-exp_binary64_3198` `add-log-exp_binary64_3186` `div-inv_binary64_3144`
3×	`clear-num_binary64_3146` `frac-2neg_binary64_3158` `cbrt-undiv_binary64_3181` `pow-unpow_binary64_3224`
2×	`pow-exp_binary64_3215`
1×	`pow-to-exp_binary64_3216` `sqr-pow_binary64_3119` `unpow1/3_binary64_3214` `pow-pow_binary64_3219`

Counts

4 → 124

Calls

4 calls:

10.0ms	(pow.f64 (/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d))) 1/3)
10.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))
9.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))
9.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))

series932.0ms (15.3%)

Counts

4 → 12

Calls

4 calls:

417.0ms	(pow.f64 (/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d))) 1/3)
182.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))
168.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))
166.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))

simplify83.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5191	4020

prune172.0ms (2.8%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	0	8	8
Picked	1	0	1
Done	0	3	3
Total	136	12	148

Merged error: 24.2b

Counts

148 → 12

Compiler

Compiled 8135 to 848 computations (89.6% saved)

regimes347.0ms (5.7%)

Compiler: Compiled 5201 to 2594 computations (50.1% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	38
1	18	38

end0.0ms (0%)

sample1.2s (19.6%)

Algorithm

1×

intervals

Results

341.0ms	8000×	body	128	valid
21.0ms	494×	body	128	invalid

Compiler

Compiled 1070 to 538 computations (49.7% saved)

Details

analyze728.0ms (11.9%)

sample24.0ms (0.4%)

simplify166.0ms (2.7%)

prune2.0ms (0%)

localize10.0ms (0.2%)

rewrite25.0ms (0.4%)

series307.0ms (5%)

simplify44.0ms (0.7%)

prune77.0ms (1.3%)

localize13.0ms (0.2%)

rewrite33.0ms (0.5%)

series410.0ms (6.7%)

simplify66.0ms (1.1%)

prune97.0ms (1.6%)

localize18.0ms (0.3%)

rewrite57.0ms (0.9%)

series944.0ms (15.5%)

simplify97.0ms (1.6%)

prune169.0ms (2.8%)

localize21.0ms (0.3%)

rewrite60.0ms (1%)

series932.0ms (15.3%)

simplify83.0ms (1.4%)

prune172.0ms (2.8%)

regimes347.0ms (5.7%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.2s (19.6%)

Profiling