Details

analyze169.0ms (1.9%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5512	47
0	1	1
1	1	1

Search

True	Other	False	Iter
0%	25%	75%	0
0%	25%	75%	1
0%	12.5%	87.5%	2
0%	6.3%	93.7%	3
0%	3.1%	96.9%	4
0%	1.6%	98.4%	5
0%	0.8%	99.2%	6
0%	0.4%	99.6%	7
0%	0.2%	99.8%	8
0.1%	0.1%	99.8%	9
0.1%	0%	99.9%	10
0.1%	0%	99.9%	11
0.1%	0%	99.9%	12
0.1%	0%	99.9%	13
0.1%	0%	99.9%	14

Compiler

Compiled 106 to 71 computations (33% saved)

sample77.0ms (0.9%)

Algorithm

1×

intervals

Results

57.0ms	256×	body	128	valid
8.0ms	258×	pre	128	true
0.0ms	2×	body	128	invalid

Compiler

Compiled 209 to 141 computations (32.5% saved)

simplify75.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	5512	47

prune9.0ms (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

Error

2.6b

Counts

2 → 2

Compiler

Compiled 163 to 111 computations (31.9% saved)

localize23.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
0.4b	(/.f64 (exp.f64 (*.f64 x x)) (sqrt.f64 PI.f64))
1.0b	(sqrt.f64 PI.f64)
2.7b	(exp.f64 (*.f64 x x))

rewrite28.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`*-un-lft-identity_binary64_3147`
23×	`add-sqr-sqrt_binary64_3169`
22×	`times-frac_binary64_3153` `add-cube-cbrt_binary64_3182`
15×	`sqrt-prod_binary64_3163`
11×	`add-cbrt-cube_binary64_3183`
10×	`add-exp-log_binary64_3185`
7×	`associate-/r_binary64_3091` `associate-/l_binary64_3092`
6×	`add-log-exp_binary64_3186`
5×	`pow1_binary64_3208`
3×	`cbrt-undiv_binary64_3181` `div-exp_binary64_3198`
2×	`clear-num_binary64_3146` `frac-2neg_binary64_3158` `associate-/l/_binary64_3094` `distribute-lft-out_binary64_3098` `div-inv_binary64_3144`
1×	`flip-+_binary64_3121` `flip3-+_binary64_3150` `rem-sqrt-square_binary64_3160` `prod-exp_binary64_3196` `exp-prod_binary64_3199` `sqrt-pow1_binary64_3165` `pow1/2_binary64_3227` `rem-exp-log_binary64_3187` `cbrt-unprod_binary64_3180` `exp-to-pow_binary64_3209`

Counts

4 → 87

Calls

4 calls:

10.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
5.0ms	(/.f64 (exp.f64 (*.f64 x x)) (sqrt.f64 PI.f64))
2.0ms	(exp.f64 (*.f64 x x))
1.0ms	(sqrt.f64 PI.f64)

series97.0ms (1.1%)

Counts

4 → 10

Calls

4 calls:

51.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
38.0ms	(/.f64 (exp.f64 (*.f64 x x)) (sqrt.f64 PI.f64))
8.0ms	(exp.f64 (*.f64 x x))
0.0ms	(sqrt.f64 PI.f64)

simplify70.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4914	1650
1	4914	1650

prune188.0ms (2.1%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	81	16	97
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	82	17	99

Error

0.5b

Counts

99 → 17

Compiler

Compiled 4227 to 2119 computations (49.9% saved)

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (/.f64 1 PI.f64)))
0.4b	(.f64 (/.f64 (.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (/.f64 1 PI.f64))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
0.4b	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
1.1b	(pow.f64 (exp.f64 x) x)

rewrite80.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`add-sqr-sqrt_binary64_3169`
34×	`*-un-lft-identity_binary64_3147`
28×	`add-exp-log_binary64_3185`
22×	`times-frac_binary64_3153` `add-cube-cbrt_binary64_3182` `sqrt-prod_binary64_3163`
21×	`associate-r_binary64_3087`
20×	`add-cbrt-cube_binary64_3183`
14×	`associate-l_binary64_3088`
13×	`unswap-sqr_binary64_3115`
12×	`prod-exp_binary64_3196`
10×	`unpow-prod-down_binary64_3226`
7×	`pow1_binary64_3208`
6×	`sqr-pow_binary64_3119` `cbrt-unprod_binary64_3180` `div-exp_binary64_3198`
5×	`distribute-lft-out_binary64_3098`
4×	`cbrt-undiv_binary64_3181` `add-log-exp_binary64_3186` `associate-/l*_binary64_3092` `pow-pow_binary64_3219`
3×	`pow-exp_binary64_3215` `flip-+_binary64_3121` `flip3-+_binary64_3150` `pow-to-exp_binary64_3216` `exp-prod_binary64_3199` `pow-unpow_binary64_3224` `associate-*r/_binary64_3089` `div-inv_binary64_3144`
2×	`*-commutative_binary64_3078` `frac-times_binary64_3157` `associate-/l/_binary64_3094`
1×	`clear-num_binary64_3146` `pow-prod-down_binary64_3218` `associate-l/_binary64_3090` `frac-2neg_binary64_3158` `associate-/r_binary64_3091` `distribute-lft-in_binary64_3096` `distribute-rgt-in_binary64_3097` `sqrt-div_binary64_3164`

Counts

4 → 130

Calls

4 calls:

39.0ms	(.f64 (/.f64 (.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (/.f64 1 PI.f64))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
12.0ms	(*.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (/.f64 1 PI.f64)))
10.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
4.0ms	(pow.f64 (exp.f64 x) x)

series239.0ms (2.6%)

Counts

4 → 12

Calls

4 calls:

117.0ms	(.f64 (/.f64 (.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (/.f64 1 PI.f64))) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
53.0ms	(*.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (/.f64 1 PI.f64)))
49.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
21.0ms	(pow.f64 (exp.f64 x) x)

simplify103.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4942	4004
1	4942	4004

prune342.0ms (3.8%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	129	13	142
Fresh	4	12	16
Picked	1	0	1
Done	0	0	0
Total	134	25	159

Error

0.2b

Counts

159 → 25

Compiler

Compiled 6873 to 4096 computations (40.4% saved)

localize36.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
0.4b	(.f64 (.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (/.f64 1 PI.f64))) (+.f64 1 (pow.f64 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6))) 3)))
0.7b	(pow.f64 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6))) 3)
1.1b	(pow.f64 (exp.f64 x) x)

rewrite99.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`*-un-lft-identity_binary64_3147`
19×	`add-exp-log_binary64_3185`
15×	`add-cbrt-cube_binary64_3183`
13×	`add-sqr-sqrt_binary64_3169` `add-cube-cbrt_binary64_3182`
8×	`pow1_binary64_3208` `prod-exp_binary64_3196`
7×	`unpow-prod-down_binary64_3226`
6×	`pow-unpow_binary64_3224`
5×	`distribute-lft-out_binary64_3098` `pow-pow_binary64_3219` `associate-*r/_binary64_3089`
4×	`times-frac_binary64_3153` `flip-+_binary64_3121` `associate-r_binary64_3087` `flip3-+_binary64_3150` `cube-prod_binary64_3175` `cbrt-unprod_binary64_3180` `add-log-exp_binary64_3186` `associate-/l*_binary64_3092`
3×	`pow-exp_binary64_3215` `pow-to-exp_binary64_3216` `exp-prod_binary64_3199` `cube-div_binary64_3176` `sqrt-div_binary64_3164`
2×	`frac-times_binary64_3157` `associate-/l/_binary64_3094` `sqr-pow_binary64_3119` `cbrt-undiv_binary64_3181` `div-exp_binary64_3198`
1×	`-commutative_binary64_3078` `frac-add_binary64_3155` `clear-num_binary64_3146` `pow-prod-down_binary64_3218` `associate-l/_binary64_3090` `rem-cube-cbrt_binary64_3170` `frac-2neg_binary64_3158` `associate-/r_binary64_3091` `distribute-lft-in_binary64_3096` `cube-mult_binary64_3177` `associate-l*_binary64_3088` `distribute-rgt-in_binary64_3097` `unpow3_binary64_3213` `div-inv_binary64_3144`

Counts

4 → 100

Calls

4 calls:

42.0ms	(.f64 (.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (/.f64 1 PI.f64))) (+.f64 1 (pow.f64 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6))) 3)))
24.0ms	(pow.f64 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6))) 3)
10.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
4.0ms	(pow.f64 (exp.f64 x) x)

series248.0ms (2.7%)

Counts

4 → 12

Calls

4 calls:

143.0ms	(.f64 (.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (/.f64 1 PI.f64))) (+.f64 1 (pow.f64 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6))) 3)))
51.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
32.0ms	(pow.f64 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) (/.f64 15/8 (pow.f64 x 6))) 3)
22.0ms	(pow.f64 (exp.f64 x) x)

simplify68.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5701	3345

prune588.0ms (6.5%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	106	6	112
Fresh	5	19	24
Picked	1	0	1
Done	0	0	0
Total	112	25	137

Error

0.2b

Counts

137 → 25

Compiler

Compiled 10699 to 6813 computations (36.3% saved)

localize25.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (sqrt.f64 (pow.f64 (exp.f64 x) x)) (sqrt.f64 (pow.f64 (exp.f64 x) x)))
1.0b	(sqrt.f64 PI.f64)
1.1b	(pow.f64 (exp.f64 x) x)
1.1b	(pow.f64 (exp.f64 x) x)

rewrite41.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

57×	`sqrt-prod_binary64_3163`
56×	`add-sqr-sqrt_binary64_3169`
28×	`unpow-prod-down_binary64_3226`
23×	`*-un-lft-identity_binary64_3147` `add-cube-cbrt_binary64_3182`
16×	`unswap-sqr_binary64_3115` `sqr-pow_binary64_3119`
14×	`pow1_binary64_3208`
12×	`swap-sqr_binary64_3114`
10×	`associate-r_binary64_3087` `associate-l_binary64_3088`
8×	`pow-pow_binary64_3219`
7×	`rem-sqrt-square_binary64_3160` `sqrt-pow1_binary64_3165` `pow1/2_binary64_3227`
6×	`add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183` `exp-prod_binary64_3199` `pow-unpow_binary64_3224`
4×	`add-log-exp_binary64_3186`
3×	`pow-prod-down_binary64_3218` `sqr-abs_binary64_3162` `pow-prod-up_binary64_3217` `pow-sqr_binary64_3120`
2×	`pow-exp_binary64_3215` `pow-to-exp_binary64_3216`
1×	`*-commutative_binary64_3078` `sqrt-unprod_binary64_3167` `prod-exp_binary64_3196` `pow-plus_binary64_3210` `pow2_binary64_3228` `cbrt-unprod_binary64_3180` `rem-square-sqrt_binary64_3159`

Counts

4 → 127

Calls

4 calls:

13.0ms	(*.f64 (sqrt.f64 (pow.f64 (exp.f64 x) x)) (sqrt.f64 (pow.f64 (exp.f64 x) x)))
4.0ms	(pow.f64 (exp.f64 x) x)
3.0ms	(pow.f64 (exp.f64 x) x)
1.0ms	(sqrt.f64 PI.f64)

series60.0ms (0.7%)

Counts

4 → 10

Calls

4 calls:

21.0ms	(*.f64 (sqrt.f64 (pow.f64 (exp.f64 x) x)) (sqrt.f64 (pow.f64 (exp.f64 x) x)))
20.0ms	(pow.f64 (exp.f64 x) x)
19.0ms	(pow.f64 (exp.f64 x) x)
0.0ms	(sqrt.f64 PI.f64)

simplify72.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4964	1695
1	4964	1695

prune221.0ms (2.4%)

Pruning

30 alts after pruning (29 fresh and 1 done)

	Pruned	Kept	Total
New	128	9	137
Fresh	4	20	24
Picked	0	1	1
Done	0	0	0
Total	132	30	162

Error

0.1b

Counts

162 → 30

Compiler

Compiled 5459 to 2377 computations (56.5% saved)

regimes873.0ms (9.7%)

Accuracy

Total 1.1b remaining (88.3%)

Threshold costs 0b (0%)

Compiler

Compiled 13691 to 9243 computations (32.5% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	69
1	30	69

end0.0ms (0%)

sample5.2s (57.4%)

Algorithm

1×

intervals

Results

1.8s	8000×	body	128	valid
107.0ms	8099×	pre	128	true
22.0ms	99×	body	128	invalid

Compiler

Compiled 4642 to 3133 computations (32.5% saved)

Details

analyze169.0ms (1.9%)

sample77.0ms (0.9%)

simplify75.0ms (0.8%)

prune9.0ms (0.1%)

localize23.0ms (0.3%)

rewrite28.0ms (0.3%)

series97.0ms (1.1%)

simplify70.0ms (0.8%)

prune188.0ms (2.1%)

localize24.0ms (0.3%)

rewrite80.0ms (0.9%)

series239.0ms (2.6%)

simplify103.0ms (1.1%)

prune342.0ms (3.8%)

localize36.0ms (0.4%)

rewrite99.0ms (1.1%)

series248.0ms (2.7%)

simplify68.0ms (0.7%)

prune588.0ms (6.5%)

localize25.0ms (0.3%)

rewrite41.0ms (0.5%)

series60.0ms (0.7%)

simplify72.0ms (0.8%)

prune221.0ms (2.4%)

regimes873.0ms (9.7%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample5.2s (57.4%)

Profiling