Details

analyze2.3s (3.1%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4804	115
1	4804	115
0	1	1
1	1	1

Search

True	Other	False	Iter
0%	74.9%	25.1%	0
0%	74.9%	25.1%	1
0%	74.9%	25.1%	2
18.7%	56.2%	25.1%	3
37.5%	37.5%	25.1%	4
42.1%	32.8%	25.1%	5
46.8%	28.1%	25.1%	6
48%	26.9%	25.1%	7
49.2%	25.8%	25.1%	8
49.5%	25.5%	25.1%	9
49.8%	25.2%	25.1%	10
49.8%	25.2%	25.1%	11
49.8%	25.1%	25.1%	12
49.9%	25%	25.1%	13
49.9%	25%	25.1%	14

Compiler

Compiled 126 to 112 computations (11.1% saved)

sample2.0s (2.7%)

Algorithm

1×

intervals

Results

1.9s	138×	body	8192	exit
98.0ms	256×	body	128	valid
9.0ms	395×	pre	128	true
0.0ms	1×	body	128	invalid

Compiler

Compiled 249 to 223 computations (10.4% saved)

simplify67.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4804	115
1	4804	115

prune12.0ms (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

Error

1.8b

Counts

2 → 2

Compiler

Compiled 271 to 232 computations (14.4% saved)

localize83.0ms (0.1%)

Local error

Found 4 expressions with local error:

6.6b	(-.f64 (-.f64 1 z) 1)
6.6b	(-.f64 (-.f64 1 z) 1)
6.6b	(-.f64 (-.f64 1 z) 1)
6.6b	(-.f64 (-.f64 1 z) 1)

rewrite1.6s (2%)

Algorithm

1×	rewrite-expression-head

Error

1.8b

Rules

36×	`*-un-lft-identity_binary64_3147`
28×	`add-sqr-sqrt_binary64_3169`
24×	`add-log-exp_binary64_3186` `cancel-sign-sub-inv_binary64_3113`
16×	`associate--l+_binary64_3084`
12×	`diff-log_binary64_3239` `add-cube-cbrt_binary64_3182` `distribute-lft-out--_binary64_3099`
8×	`sub-neg_binary64_3140` `difference-of-squares_binary64_3116`
4×	`pow1_binary64_3208` `add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183` `flip3--_binary64_3151` `flip--_binary64_3122` `difference-of-sqr-1_binary64_3117` `associate--l-_binary64_3085`

Counts

4 → 100

Calls

4 calls:

17.0ms	(-.f64 (-.f64 1 z) 1)
16.0ms	(-.f64 (-.f64 1 z) 1)
16.0ms	(-.f64 (-.f64 1 z) 1)
16.0ms	(-.f64 (-.f64 1 z) 1)

Compiler

Compiled 12896 to 10998 computations (14.7% saved)

series245.0ms (0.3%)

Error

1.8b

Counts

4 → 12

Calls

4 calls:

51.0ms	(-.f64 (-.f64 1 z) 1)
47.0ms	(-.f64 (-.f64 1 z) 1)
42.0ms	(-.f64 (-.f64 1 z) 1)
37.0ms	(-.f64 (-.f64 1 z) 1)

Compiler

Compiled 4356 to 3833 computations (12% saved)

simplify87.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	5392	704

prune1.3s (1.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	112	2	114

Error

1.8b

Counts

114 → 2

Compiler

Compiled 13990 to 11821 computations (15.5% saved)

localize61.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
1.0b	(+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))
1.0b	(sqrt.f64 (*.f64 PI.f64 2))
2.6b	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))

rewrite541.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

1.1b

Rules

19×	`*-un-lft-identity_binary64_3147`
18×	`add-log-exp_binary64_3186`
10×	`add-exp-log_binary64_3185`
9×	`sum-log_binary64_3238` `pow1_binary64_3208` `add-cbrt-cube_binary64_3183` `distribute-lft-out_binary64_3098`
8×	`frac-add_binary64_3155`
7×	`prod-exp_binary64_3196`
5×	`add-cube-cbrt_binary64_3182` `add-sqr-sqrt_binary64_3169` `flip3-+_binary64_3150` `flip-+_binary64_3121`
4×	`associate-r_binary64_3087`
3×	`cbrt-unprod_binary64_3180`
2×	`associate-+l+_binary64_3080` `+-commutative_binary64_3077` `pow-prod-down_binary64_3218` `sqrt-pow1_binary64_3165`
1×	`pow1/2_binary64_3227` `sqrt-prod_binary64_3163` `pow-to-exp_binary64_3216` `pow-exp_binary64_3215` `pow-sub_binary64_3223` `associate-r/_binary64_3089` `associate-l/_binary64_3090` `associate-l_binary64_3088` `exp-sum_binary64_3193` `*-commutative_binary64_3078`

Counts

4 → 70

Calls

4 calls:

45.0ms	(+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))
22.0ms	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))
16.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
2.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 6200 to 4800 computations (22.6% saved)

series411.0ms (0.5%)

Error

1.1b

Counts

4 → 20

Calls

4 calls:

228.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
52.0ms	(+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))
45.0ms	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 3676 to 2954 computations (19.6% saved)

simplify78.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5563	2799

prune545.0ms (0.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	84	6	90
Fresh	0	0	0
Picked	1	0	1
Done	1	0	1
Total	86	6	92

Error

1.1b

Counts

92 → 6

Compiler

Compiled 8028 to 6206 computations (22.7% saved)

localize67.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b	(+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))) (/.f64 848079078717083/1099511627776 (-.f64 3 z))) (/.f64 -6214088902520669/35184372088832 (-.f64 4 z)))
1.0b	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
1.0b	(+.f64 (+.f64 562949953421205/562949953421312 (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))
1.0b	(sqrt.f64 (*.f64 PI.f64 2))

rewrite661.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

28×	`*-un-lft-identity_binary64_3147`
27×	`add-log-exp_binary64_3186`
16×	`sum-log_binary64_3238` `distribute-lft-out_binary64_3098`
10×	`add-exp-log_binary64_3185`
9×	`pow1_binary64_3208` `add-cbrt-cube_binary64_3183`
8×	`frac-add_binary64_3155`
7×	`prod-exp_binary64_3196`
5×	`add-cube-cbrt_binary64_3182` `add-sqr-sqrt_binary64_3169` `flip3-+_binary64_3150` `flip-+_binary64_3121`
4×	`associate-r_binary64_3087`
3×	`cbrt-unprod_binary64_3180`
2×	`pow-prod-down_binary64_3218` `sqrt-pow1_binary64_3165` `associate-+l+_binary64_3080` `+-commutative_binary64_3077`
1×	`pow1/2_binary64_3227` `sqrt-prod_binary64_3163` `pow-to-exp_binary64_3216` `pow-exp_binary64_3215` `pow-sub_binary64_3223` `associate-r/_binary64_3089` `associate-l/_binary64_3090` `associate-l_binary64_3088` `exp-sum_binary64_3193` `*-commutative_binary64_3078`

Counts

4 → 74

Calls

4 calls:

78.0ms	(+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))) (/.f64 848079078717083/1099511627776 (-.f64 3 z))) (/.f64 -6214088902520669/35184372088832 (-.f64 4 z)))
60.0ms	(+.f64 (+.f64 562949953421205/562949953421312 (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))
24.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
2.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 6817 to 5294 computations (22.3% saved)

series412.0ms (0.5%)

Error

1.1b

Counts

4 → 20

Calls

4 calls:

205.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
70.0ms	(+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))) (/.f64 848079078717083/1099511627776 (-.f64 3 z))) (/.f64 -6214088902520669/35184372088832 (-.f64 4 z)))
57.0ms	(+.f64 (+.f64 562949953421205/562949953421312 (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 3508 to 2814 computations (19.8% saved)

simplify146.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (92.0ms)

Iter	Nodes	Cost
0	4913	3566
1	4913	3566

prune633.0ms (0.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	90	4	94
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	92	8	100

Error

0.2b

Counts

100 → 8

Compiler

Compiled 8697 to 6745 computations (22.4% saved)

localize81.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b	(+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))) (/.f64 848079078717083/1099511627776 (-.f64 3 z))) (/.f64 -6214088902520669/35184372088832 (-.f64 4 z)))
1.0b	(.f64 (.f64 (*.f64 (sqrt.f64 PI.f64) (sqrt.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
1.0b	(+.f64 (+.f64 562949953421205/562949953421312 (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))
1.0b	(sqrt.f64 PI.f64)

rewrite742.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

29×	`*-un-lft-identity_binary64_3147`
27×	`add-log-exp_binary64_3186`
18×	`add-exp-log_binary64_3185`
16×	`sum-log_binary64_3238` `distribute-lft-out_binary64_3098` `prod-exp_binary64_3196`
13×	`add-cbrt-cube_binary64_3183`
8×	`frac-add_binary64_3155`
7×	`pow1_binary64_3208` `add-sqr-sqrt_binary64_3169`
6×	`add-cube-cbrt_binary64_3182` `cbrt-unprod_binary64_3180`
5×	`flip3-+_binary64_3150` `flip-+_binary64_3121`
4×	`associate-r_binary64_3087`
3×	`sqrt-prod_binary64_3163`
2×	`associate-+l+_binary64_3080` `+-commutative_binary64_3077` `pow-to-exp_binary64_3216` `pow-exp_binary64_3215`
1×	`pow1/2_binary64_3227` `sqrt-pow1_binary64_3165` `rem-sqrt-square_binary64_3160` `pow-prod-down_binary64_3218` `pow-sub_binary64_3223` `associate-r/_binary64_3089` `associate-l/_binary64_3090` `associate-l_binary64_3088` `exp-sum_binary64_3193` `*-commutative_binary64_3078`

Counts

4 → 80

Calls

4 calls:

73.0ms	(+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))) (/.f64 848079078717083/1099511627776 (-.f64 3 z))) (/.f64 -6214088902520669/35184372088832 (-.f64 4 z)))
52.0ms	(+.f64 (+.f64 562949953421205/562949953421312 (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))
36.0ms	(.f64 (.f64 (*.f64 (sqrt.f64 PI.f64) (sqrt.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
1.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 7401 to 5653 computations (23.6% saved)

series405.0ms (0.5%)

Error

0.2b

Counts

4 → 20

Calls

4 calls:

208.0ms	(.f64 (.f64 (*.f64 (sqrt.f64 PI.f64) (sqrt.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
72.0ms	(+.f64 (+.f64 562949953421205/562949953421312 (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))
45.0ms	(+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))) (/.f64 848079078717083/1099511627776 (-.f64 3 z))) (/.f64 -6214088902520669/35184372088832 (-.f64 4 z)))
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 3540 to 2832 computations (20% saved)

simplify128.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	4922	3722
1	4922	3722

prune608.0ms (0.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	98	2	100
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	100	8	108

Error

0.2b

Counts

108 → 8

Compiler

Compiled 8427 to 6394 computations (24.1% saved)

regimes938.0ms (1.2%)

Accuracy

Total 0.2b remaining (39%)

Threshold costs 0.2b (39%)

Compiler

Compiled 11390 to 9526 computations (16.4% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	106	119
1	106	119

end0.0ms (0%)

sample1.0min (81.3%)

Algorithm

1×

intervals

Results

52.9s	3839×	body	8192	exit
3.0s	8000×	body	128	valid
254.0ms	11915×	pre	128	true
30.0ms	76×	body	128	invalid

Compiler

Compiled 5773 to 4828 computations (16.4% saved)

Details

analyze2.3s (3.1%)

sample2.0s (2.7%)

simplify67.0ms (0.1%)

prune12.0ms (0%)

localize83.0ms (0.1%)

rewrite1.6s (2%)

series245.0ms (0.3%)

simplify87.0ms (0.1%)

prune1.3s (1.7%)

localize61.0ms (0.1%)

rewrite541.0ms (0.7%)

series411.0ms (0.5%)

simplify78.0ms (0.1%)

prune545.0ms (0.7%)

localize67.0ms (0.1%)

rewrite661.0ms (0.9%)

series412.0ms (0.5%)

simplify146.0ms (0.2%)

prune633.0ms (0.8%)

localize81.0ms (0.1%)

rewrite742.0ms (1%)

series405.0ms (0.5%)

simplify128.0ms (0.2%)

prune608.0ms (0.8%)

regimes938.0ms (1.2%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample1.0min (81.3%)

Profiling