Details

analyze467.0ms (8.6%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4908	36
1	4908	36
0	2	2
1	2	2

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	68.7%	12.6%	6
28.1%	59.3%	12.6%	7
32.8%	48.4%	18.8%	8
38.2%	42.9%	18.8%	9
41%	37.1%	22%	10
43.9%	34.1%	22%	11
45.5%	31%	23.5%	12
46.9%	29.6%	23.5%	13
47.7%	28%	24.3%	14

Compiler

Compiled 17 to 9 computations (47.1% saved)

sample46.0ms (0.9%)

Algorithm

1×

intervals

Results

25.0ms	112×	body	8192	exit
7.0ms	211×	body	128	valid
3.0ms	24×	body	512	valid
1.0ms	21×	body	256	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 33 to 19 computations (42.4% saved)

simplify138.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (132.0ms)

Iter	Nodes	Cost
0	4887	18
1	4887	18

prune4.0ms (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: 12.1b

Counts

2 → 2

Compiler

Compiled 40 to 26 computations (35% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 x (exp.f64 wj))
0.0b	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
3.9b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))

rewrite41.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

49×	`*-un-lft-identity_binary64_3147`
48×	`add-sqr-sqrt_binary64_3169`
38×	`times-frac_binary64_3153`
23×	`add-cube-cbrt_binary64_3182`
10×	`difference-of-squares_binary64_3116`
9×	`associate-/l*_binary64_3092`
8×	`distribute-lft-out_binary64_3098`
7×	`add-cbrt-cube_binary64_3183` `associate-/r*_binary64_3091`
6×	`add-exp-log_binary64_3185`
5×	`distribute-lft-out--_binary64_3099` `add-log-exp_binary64_3186`
3×	`pow1_binary64_3208`
2×	`clear-num_binary64_3146` `flip-+_binary64_3121` `frac-2neg_binary64_3158` `flip3-+_binary64_3150` `associate-/l/_binary64_3094` `div-sub_binary64_3152` `cbrt-undiv_binary64_3181` `div-exp_binary64_3198` `associate-/r/_binary64_3093` `div-inv_binary64_3144`
1×	`flip--_binary64_3122` `flip3--_binary64_3151` `associate-+r-_binary64_3081` `+-commutative_binary64_3077` `sum-log_binary64_3238`

Counts

3 → 91

Calls

3 calls:

17.0ms	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
13.0ms	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
4.0ms	(/.f64 x (exp.f64 wj))

series121.0ms (2.2%)

Counts

3 → 9

Calls

3 calls:

45.0ms	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
42.0ms	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
33.0ms	(/.f64 x (exp.f64 wj))

simplify73.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4946	2095
1	4946	2095

prune103.0ms (1.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	95	5	100
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	96	6	102

Merged error: 0.3b

Counts

102 → 6

Compiler

Compiled 2114 to 864 computations (59.1% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(.f64 wj (+.f64 wj (.f64 x -2)))
0.0b	(+.f64 x (.f64 wj (+.f64 wj (.f64 x -2))))

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64_3169`
4×	`*-un-lft-identity_binary64_3147` `add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183` `pow1_binary64_3208` `add-log-exp_binary64_3186` `add-cube-cbrt_binary64_3182`
3×	`associate-r_binary64_3087` `associate-l_binary64_3088`
2×	`flip-+_binary64_3121` `flip3-+_binary64_3150` `distribute-lft-in_binary64_3096` `associate-+r+_binary64_3079` `distribute-rgt-in_binary64_3097` `associate-*r/_binary64_3089`
1×	`*-commutative_binary64_3078` `unswap-sqr_binary64_3115` `pow-prod-down_binary64_3218` `+-commutative_binary64_3077` `prod-exp_binary64_3196` `cbrt-unprod_binary64_3180` `sum-log_binary64_3238`

Counts

2 → 35

Calls

2 calls:

5.0ms	(.f64 wj (+.f64 wj (.f64 x -2)))
4.0ms	(+.f64 x (.f64 wj (+.f64 wj (.f64 x -2))))

series58.0ms (1.1%)

Counts

2 → 6

Calls

2 calls:

30.0ms	(+.f64 x (.f64 wj (+.f64 wj (.f64 x -2))))
28.0ms	(.f64 wj (+.f64 wj (.f64 x -2)))

simplify55.0ms (1%)

Algorithm

1×	egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4970	598
1	4970	598

prune42.0ms (0.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	39	2	41
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	39	8	47

Merged error: 0.3b

Counts

47 → 8

Compiler

Compiled 762 to 455 computations (40.3% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(.f64 (cbrt.f64 (+.f64 wj (.f64 x -2))) (cbrt.f64 (+.f64 wj (*.f64 x -2))))
0.5b	(cbrt.f64 (+.f64 wj (*.f64 x -2)))
0.5b	(cbrt.f64 (+.f64 wj (*.f64 x -2)))
0.5b	(cbrt.f64 (+.f64 wj (*.f64 x -2)))

rewrite26.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`cbrt-prod_binary64_3178`
23×	`add-sqr-sqrt_binary64_3169`
18×	`cbrt-div_binary64_3179`
15×	`*-un-lft-identity_binary64_3147` `add-cube-cbrt_binary64_3182`
11×	`pow1_binary64_3208`
9×	`pow1/3_binary64_3229` `flip-+_binary64_3121` `flip3-+_binary64_3150`
6×	`add-exp-log_binary64_3185` `swap-sqr_binary64_3114` `associate-r_binary64_3087` `associate-l_binary64_3088`
4×	`frac-times_binary64_3157` `unswap-sqr_binary64_3115` `add-cbrt-cube_binary64_3183` `add-log-exp_binary64_3186`
2×	`pow-prod-down_binary64_3218` `associate-l/_binary64_3090` `pow-prod-up_binary64_3217` `associate-r/_binary64_3089` `pow-sqr_binary64_3120`
1×	`*-commutative_binary64_3078` `prod-exp_binary64_3196` `pow-plus_binary64_3210` `pow2_binary64_3228` `cbrt-unprod_binary64_3180`

Counts

4 → 87

Calls

4 calls:

10.0ms	(.f64 (cbrt.f64 (+.f64 wj (.f64 x -2))) (cbrt.f64 (+.f64 wj (*.f64 x -2))))
3.0ms	(cbrt.f64 (+.f64 wj (*.f64 x -2)))
2.0ms	(cbrt.f64 (+.f64 wj (*.f64 x -2)))
2.0ms	(cbrt.f64 (+.f64 wj (*.f64 x -2)))

series484.0ms (8.9%)

Counts

4 → 12

Calls

4 calls:

128.0ms	(cbrt.f64 (+.f64 wj (*.f64 x -2)))
127.0ms	(.f64 (cbrt.f64 (+.f64 wj (.f64 x -2))) (cbrt.f64 (+.f64 wj (*.f64 x -2))))
119.0ms	(cbrt.f64 (+.f64 wj (*.f64 x -2)))
110.0ms	(cbrt.f64 (+.f64 wj (*.f64 x -2)))

simplify70.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4901	1786
1	4901	1786

prune148.0ms (2.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	98	1	99
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	98	9	107

Merged error: 0.3b

Counts

107 → 9

Compiler

Compiled 3107 to 2136 computations (31.3% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj))
0.6b	(cbrt.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj))
0.6b	(cbrt.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj))
9.6b	(+.f64 wj (.f64 (.f64 (cbrt.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj)) (cbrt.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj))) (/.f64 (cbrt.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj)) (+.f64 wj 1))))

rewrite32.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64_3169`
18×	`cbrt-prod_binary64_3178`
13×	`*-un-lft-identity_binary64_3147`
7×	`add-cube-cbrt_binary64_3182`
6×	`cbrt-div_binary64_3179` `difference-of-squares_binary64_3116` `add-log-exp_binary64_3186`
4×	`add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183` `pow1_binary64_3208`
3×	`times-frac_binary64_3153` `flip--_binary64_3122` `pow1/3_binary64_3229` `flip3--_binary64_3151` `distribute-lft-out--_binary64_3099`
1×	`flip-+_binary64_3121` `flip3-+_binary64_3150` `+-commutative_binary64_3077` `sum-log_binary64_3238`

Counts

4 → 59

Calls

4 calls:

7.0ms	(cbrt.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj))
7.0ms	(cbrt.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj))
7.0ms	(cbrt.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj))
3.0ms	(+.f64 wj (.f64 (.f64 (cbrt.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj)) (cbrt.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj))) (/.f64 (cbrt.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj)) (+.f64 wj 1))))

series865.0ms (15.9%)

Counts

4 → 12

Calls

4 calls:

280.0ms	(cbrt.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj))
276.0ms	(cbrt.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj))
264.0ms	(cbrt.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj))
45.0ms	(+.f64 wj (.f64 (.f64 (cbrt.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj)) (cbrt.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj))) (/.f64 (cbrt.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj)) (+.f64 wj 1))))

simplify77.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5224	1487

prune76.0ms (1.4%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	71	9	80

Merged error: 0.3b

Counts

80 → 9

Compiler

Compiled 2408 to 617 computations (74.4% saved)

regimes267.0ms (4.9%)

Compiler: Compiled 2565 to 1593 computations (37.9% saved)

bsearch36.0ms (0.7%)

Steps

Iters	Range		Point
8	1.7675736608990216e-10	8.05857331537012e-07	8.586694722522736e-09
8	-7.110368521444943e-05	-3.4068612930480263e-09	-5.070275397261289e-09

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	47	63
1	47	63

end0.0ms (0%)

sample2.2s (39.7%)

Algorithm

1×

intervals

Results

830.0ms	3784×	body	8192	exit
248.0ms	6540×	body	128	valid
78.0ms	696×	body	512	valid
53.0ms	735×	body	256	valid
5.0ms	29×	body	1024	valid
3.0ms	67×	body	128	invalid
0.0ms	10×	body	128	overflowed

Compiler

Compiled 919 to 573 computations (37.6% saved)

Details

analyze467.0ms (8.6%)

sample46.0ms (0.9%)

simplify138.0ms (2.5%)

prune4.0ms (0.1%)

localize8.0ms (0.1%)

rewrite41.0ms (0.8%)

series121.0ms (2.2%)

simplify73.0ms (1.4%)

prune103.0ms (1.9%)

localize6.0ms (0.1%)

rewrite11.0ms (0.2%)

series58.0ms (1.1%)

simplify55.0ms (1%)

prune42.0ms (0.8%)

localize9.0ms (0.2%)

rewrite26.0ms (0.5%)

series484.0ms (8.9%)

simplify70.0ms (1.3%)

prune148.0ms (2.7%)

localize12.0ms (0.2%)

rewrite32.0ms (0.6%)

series865.0ms (15.9%)

simplify77.0ms (1.4%)

prune76.0ms (1.4%)

regimes267.0ms (4.9%)

bsearch36.0ms (0.7%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample2.2s (39.7%)

Profiling