Details

analyze906.0ms (8.6%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4840	8
1	4840	8
0	1	1
1	1	1

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	62.5%	12.5%	4
25%	56.2%	18.8%	5
28.1%	50%	21.9%	6
29.7%	46.9%	23.5%	7
30.5%	45.3%	24.3%	8
30.8%	44.9%	24.3%	9
31.2%	44.5%	24.3%	10
31.3%	44.3%	24.4%	11
31.4%	44.3%	24.4%	12
31.4%	44%	24.5%	13
31.5%	43.8%	24.8%	14

Compiler

Compiled 13 to 12 computations (7.7% saved)

sample82.0ms (0.8%)

Algorithm

1×

intervals

Results

36.0ms	77×	body	1024	valid
11.0ms	44×	body	512	valid
8.0ms	106×	body	128	valid
5.0ms	9×	body	2048	valid
3.0ms	20×	body	256	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 25 to 24 computations (4% saved)

simplify81.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4840	8
1	4840	8

prune7.0ms (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

0.3b

Counts

2 → 2

Compiler

Compiled 22 to 21 computations (4.5% saved)

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 1 (exp.f64 x))
0.2b	(sqrt.f64 (+.f64 1 (exp.f64 x)))

rewrite52.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

0.3b

Rules

7×	`*-un-lft-identity_binary64`
4×	`add-log-exp_binary64` `add-sqr-sqrt_binary64` `sqrt-prod_binary64`
3×	`pow1_binary64` `add-cube-cbrt_binary64`
2×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `flip3-+_binary64` `sqrt-div_binary64` `flip-+_binary64` `distribute-lft-out_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `sum-log_binary64` `+-commutative_binary64`

Counts

2 → 28

Calls

2 calls:

10.0ms	(sqrt.f64 (+.f64 1 (exp.f64 x)))
4.0ms	(+.f64 1 (exp.f64 x))

Compiler

Compiled 321 to 218 computations (32.1% saved)

series97.0ms (0.9%)

Error

0.2b

Counts

2 → 12

Calls

2 calls:

65.0ms	(sqrt.f64 (+.f64 1 (exp.f64 x)))
14.0ms	(+.f64 1 (exp.f64 x))

Compiler

Compiled 324 to 294 computations (9.3% saved)

simplify44.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5074	484

prune35.0ms (0.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	38	2	40
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	38	4	42

Error

0.2b

Counts

42 → 4

Compiler

Compiled 457 to 345 computations (24.5% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (exp.f64 x) 1)
0.0b	(pow.f64 (+.f64 (exp.f64 x) 1) 3)
0.2b	(sqrt.f64 (cbrt.f64 (pow.f64 (+.f64 (exp.f64 x) 1) 3)))
0.5b	(cbrt.f64 (pow.f64 (+.f64 (exp.f64 x) 1) 3))

rewrite150.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

32×	`cbrt-prod_binary64`
28×	`*-un-lft-identity_binary64`
18×	`add-sqr-sqrt_binary64`
17×	`sqrt-prod_binary64`
14×	`add-cube-cbrt_binary64`
13×	`unpow-prod-down_binary64` `cube-prod_binary64`
7×	`distribute-lft-out_binary64`
6×	`pow1_binary64` `add-log-exp_binary64` `cube-div_binary64`
5×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `rem-sqrt-square_binary64`
4×	`flip3-+_binary64` `cbrt-div_binary64` `flip-+_binary64` `sqr-pow_binary64`
3×	`unpow3_binary64` `cube-mult_binary64` `pow-unpow_binary64`
2×	`pow1/3_binary64` `sqrt-pow1_binary64` `sqrt-div_binary64`
1×	`rem-cbrt-cube_binary64` `pow1/2_binary64` `pow-pow_binary64` `pow-to-exp_binary64` `pow-exp_binary64` `rem-cube-cbrt_binary64` `sum-log_binary64` `+-commutative_binary64`

Counts

4 → 98

Calls

4 calls:

11.0ms	(sqrt.f64 (cbrt.f64 (pow.f64 (+.f64 (exp.f64 x) 1) 3)))
8.0ms	(pow.f64 (+.f64 (exp.f64 x) 1) 3)
6.0ms	(cbrt.f64 (pow.f64 (+.f64 (exp.f64 x) 1) 3))
4.0ms	(+.f64 (exp.f64 x) 1)

Compiler

Compiled 1566 to 1197 computations (23.6% saved)

series172.0ms (1.6%)

Error

0.2b

Counts

4 → 24

Calls

4 calls:

70.0ms	(pow.f64 (+.f64 (exp.f64 x) 1) 3)
48.0ms	(sqrt.f64 (cbrt.f64 (pow.f64 (+.f64 (exp.f64 x) 1) 3)))
19.0ms	(cbrt.f64 (pow.f64 (+.f64 (exp.f64 x) 1) 3))
14.0ms	(+.f64 (exp.f64 x) 1)

Compiler

Compiled 592 to 538 computations (9.1% saved)

simplify100.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4969	1469
1	4969	1469

prune109.0ms (1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	122	0	122
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	122	4	126

Error

0.2b

Counts

126 → 4

Compiler

Compiled 1428 to 1076 computations (24.6% saved)

localize33.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.0b	(/.f64 1/16 (pow.f64 (sqrt.f64 2) 5))
1.6b	(pow.f64 (sqrt.f64 2) 5)
13.6b	(+.f64 (+.f64 (+.f64 (sqrt.f64 2) (.f64 (pow.f64 x 3) (+.f64 (/.f64 1/16 (pow.f64 (sqrt.f64 2) 5)) (/.f64 1/12 (sqrt.f64 2))))) (.f64 1/2 (/.f64 x (sqrt.f64 2)))) (.f64 (.f64 (/.f64 x (sqrt.f64 2)) x) 3/16))
17.2b	(+.f64 (+.f64 (+.f64 (+.f64 (sqrt.f64 2) (.f64 (pow.f64 x 3) (+.f64 (/.f64 1/16 (pow.f64 (sqrt.f64 2) 5)) (/.f64 1/12 (sqrt.f64 2))))) (.f64 1/2 (/.f64 x (sqrt.f64 2)))) (.f64 (.f64 (/.f64 x (sqrt.f64 2)) x) 3/16)) (*.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) -1/16))

rewrite890.0ms (8.4%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

30×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64` `unpow-prod-down_binary64` `times-frac_binary64`
27×	`add-log-exp_binary64`
22×	`associate-*l/_binary64`
18×	`frac-add_binary64`
16×	`sum-log_binary64`
15×	`sqrt-prod_binary64`
10×	`add-exp-log_binary64` `associate-/r*_binary64`
7×	`flip3-+_binary64` `flip-+_binary64`
6×	`pow1_binary64` `add-cbrt-cube_binary64`
5×	`sqr-pow_binary64`
4×	`associate-*r/_binary64`
3×	`pow-unpow_binary64` `pow-pow_binary64` `div-exp_binary64` `associate-/l*_binary64`
2×	`associate-+l+_binary64` `+-commutative_binary64` `pow-to-exp_binary64` `pow-exp_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `sqrt-pow2_binary64` `cbrt-undiv_binary64` `frac-2neg_binary64` `clear-num_binary64` `div-inv_binary64`

Counts

4 → 119

Calls

4 calls:

31.0ms	(+.f64 (+.f64 (+.f64 (+.f64 (sqrt.f64 2) (.f64 (pow.f64 x 3) (+.f64 (/.f64 1/16 (pow.f64 (sqrt.f64 2) 5)) (/.f64 1/12 (sqrt.f64 2))))) (.f64 1/2 (/.f64 x (sqrt.f64 2)))) (.f64 (.f64 (/.f64 x (sqrt.f64 2)) x) 3/16)) (*.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) -1/16))
16.0ms	(+.f64 (+.f64 (+.f64 (sqrt.f64 2) (.f64 (pow.f64 x 3) (+.f64 (/.f64 1/16 (pow.f64 (sqrt.f64 2) 5)) (/.f64 1/12 (sqrt.f64 2))))) (.f64 1/2 (/.f64 x (sqrt.f64 2)))) (.f64 (.f64 (/.f64 x (sqrt.f64 2)) x) 3/16))
8.0ms	(/.f64 1/16 (pow.f64 (sqrt.f64 2) 5))
3.0ms	(pow.f64 (sqrt.f64 2) 5)

Compiler

Compiled 8172 to 7371 computations (9.8% saved)

series270.0ms (2.6%)

Error

0.2b

Counts

4 → 16

Calls

4 calls:

134.0ms	(+.f64 (+.f64 (+.f64 (sqrt.f64 2) (.f64 (pow.f64 x 3) (+.f64 (/.f64 1/16 (pow.f64 (sqrt.f64 2) 5)) (/.f64 1/12 (sqrt.f64 2))))) (.f64 1/2 (/.f64 x (sqrt.f64 2)))) (.f64 (.f64 (/.f64 x (sqrt.f64 2)) x) 3/16))
112.0ms	(+.f64 (+.f64 (+.f64 (+.f64 (sqrt.f64 2) (.f64 (pow.f64 x 3) (+.f64 (/.f64 1/16 (pow.f64 (sqrt.f64 2) 5)) (/.f64 1/12 (sqrt.f64 2))))) (.f64 1/2 (/.f64 x (sqrt.f64 2)))) (.f64 (.f64 (/.f64 x (sqrt.f64 2)) x) 3/16)) (*.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) -1/16))
0.0ms	(pow.f64 (sqrt.f64 2) 5)
0.0ms	(/.f64 1/16 (pow.f64 (sqrt.f64 2) 5))

Compiler

Compiled 946 to 873 computations (7.7% saved)

simplify106.0ms (1%)

Algorithm

1×	egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4973	6253
1	4973	6253

prune727.0ms (6.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	134	1	135
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	135	4	139

Error

0.2b

Counts

139 → 4

Compiler

Compiled 7794 to 7029 computations (9.8% saved)

localize54.0ms (0.5%)

Local error

Found 4 expressions with local error:

1.0b	(/.f64 1/12 (sqrt.f64 2))
1.0b	(*.f64 (cbrt.f64 1/16) (cbrt.f64 1/16))
13.6b	(+.f64 (+.f64 (+.f64 (sqrt.f64 2) (.f64 (pow.f64 x 3) (+.f64 (.f64 (/.f64 (.f64 (cbrt.f64 1/16) (cbrt.f64 1/16)) (pow.f64 (sqrt.f64 (sqrt.f64 2)) 5)) (/.f64 (cbrt.f64 1/16) (pow.f64 (sqrt.f64 (sqrt.f64 2)) 5))) (/.f64 1/12 (sqrt.f64 2))))) (.f64 1/2 (/.f64 x (sqrt.f64 2)))) (.f64 (.f64 (/.f64 x (sqrt.f64 2)) x) 3/16))
17.2b	(+.f64 (+.f64 (+.f64 (+.f64 (sqrt.f64 2) (.f64 (pow.f64 x 3) (+.f64 (.f64 (/.f64 (.f64 (cbrt.f64 1/16) (cbrt.f64 1/16)) (pow.f64 (sqrt.f64 (sqrt.f64 2)) 5)) (/.f64 (cbrt.f64 1/16) (pow.f64 (sqrt.f64 (sqrt.f64 2)) 5))) (/.f64 1/12 (sqrt.f64 2))))) (.f64 1/2 (/.f64 x (sqrt.f64 2)))) (.f64 (.f64 (/.f64 x (sqrt.f64 2)) x) 3/16)) (*.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) -1/16))

rewrite1.3s (12.6%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

35×	`add-sqr-sqrt_binary64`
27×	`add-log-exp_binary64` `add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
22×	`associate-*l/_binary64`
18×	`frac-add_binary64` `times-frac_binary64`
16×	`sum-log_binary64` `cbrt-prod_binary64`
12×	`sqrt-prod_binary64`
11×	`pow1_binary64`
8×	`add-exp-log_binary64`
7×	`flip3-+_binary64` `flip-+_binary64`
6×	`add-cbrt-cube_binary64` `pow1/3_binary64` `swap-sqr_binary64` `associate-l_binary64` `associate-r_binary64` `associate-/r*_binary64`
4×	`associate-*r/_binary64` `unswap-sqr_binary64`
3×	`associate-/l*_binary64`
2×	`associate-+l+_binary64` `+-commutative_binary64` `pow-prod-down_binary64` `pow-prod-up_binary64` `pow-sqr_binary64`
1×	`pow2_binary64` `pow-plus_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `*-commutative_binary64` `div-exp_binary64` `cbrt-undiv_binary64` `frac-2neg_binary64` `clear-num_binary64` `div-inv_binary64`

Counts

4 → 118

Calls

4 calls:

15.0ms	(+.f64 (+.f64 (+.f64 (+.f64 (sqrt.f64 2) (.f64 (pow.f64 x 3) (+.f64 (.f64 (/.f64 (.f64 (cbrt.f64 1/16) (cbrt.f64 1/16)) (pow.f64 (sqrt.f64 (sqrt.f64 2)) 5)) (/.f64 (cbrt.f64 1/16) (pow.f64 (sqrt.f64 (sqrt.f64 2)) 5))) (/.f64 1/12 (sqrt.f64 2))))) (.f64 1/2 (/.f64 x (sqrt.f64 2)))) (.f64 (.f64 (/.f64 x (sqrt.f64 2)) x) 3/16)) (*.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) -1/16))
11.0ms	(+.f64 (+.f64 (+.f64 (sqrt.f64 2) (.f64 (pow.f64 x 3) (+.f64 (.f64 (/.f64 (.f64 (cbrt.f64 1/16) (cbrt.f64 1/16)) (pow.f64 (sqrt.f64 (sqrt.f64 2)) 5)) (/.f64 (cbrt.f64 1/16) (pow.f64 (sqrt.f64 (sqrt.f64 2)) 5))) (/.f64 1/12 (sqrt.f64 2))))) (.f64 1/2 (/.f64 x (sqrt.f64 2)))) (.f64 (.f64 (/.f64 x (sqrt.f64 2)) x) 3/16))
8.0ms	(/.f64 1/12 (sqrt.f64 2))
7.0ms	(*.f64 (cbrt.f64 1/16) (cbrt.f64 1/16))

Compiler

Compiled 10773 to 9977 computations (7.4% saved)

series324.0ms (3.1%)

Error

0.2b

Counts

4 → 16

Calls

4 calls:

151.0ms	(+.f64 (+.f64 (+.f64 (sqrt.f64 2) (.f64 (pow.f64 x 3) (+.f64 (.f64 (/.f64 (.f64 (cbrt.f64 1/16) (cbrt.f64 1/16)) (pow.f64 (sqrt.f64 (sqrt.f64 2)) 5)) (/.f64 (cbrt.f64 1/16) (pow.f64 (sqrt.f64 (sqrt.f64 2)) 5))) (/.f64 1/12 (sqrt.f64 2))))) (.f64 1/2 (/.f64 x (sqrt.f64 2)))) (.f64 (.f64 (/.f64 x (sqrt.f64 2)) x) 3/16))
129.0ms	(+.f64 (+.f64 (+.f64 (+.f64 (sqrt.f64 2) (.f64 (pow.f64 x 3) (+.f64 (.f64 (/.f64 (.f64 (cbrt.f64 1/16) (cbrt.f64 1/16)) (pow.f64 (sqrt.f64 (sqrt.f64 2)) 5)) (/.f64 (cbrt.f64 1/16) (pow.f64 (sqrt.f64 (sqrt.f64 2)) 5))) (/.f64 1/12 (sqrt.f64 2))))) (.f64 1/2 (/.f64 x (sqrt.f64 2)))) (.f64 (.f64 (/.f64 x (sqrt.f64 2)) x) 3/16)) (*.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) -1/16))
0.0ms	(*.f64 (cbrt.f64 1/16) (cbrt.f64 1/16))
0.0ms	(/.f64 1/12 (sqrt.f64 2))

Compiler

Compiled 1002 to 929 computations (7.3% saved)

simplify127.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4978	6469
1	4978	6469

prune996.0ms (9.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	133	1	134
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	134	4	138

Error

0.2b

Counts

138 → 4

Compiler

Compiled 9062 to 8306 computations (8.3% saved)

regimes429.0ms (4.1%)

Accuracy

Total 0.0b remaining (13%)

Threshold costs 0.0b (13%)

Compiler

Compiled 4562 to 4209 computations (7.7% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	12
1	10	12

end0.0ms (0%)

sample3.4s (32.4%)

Algorithm

1×

intervals

Results

899.0ms	2583×	body	1024	valid
262.0ms	1392×	body	512	valid
160.0ms	3067×	body	128	valid
117.0ms	293×	body	2048	valid
80.0ms	665×	body	256	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 1500 to 1385 computations (7.7% saved)

Details

analyze906.0ms (8.6%)

sample82.0ms (0.8%)

simplify81.0ms (0.8%)

prune7.0ms (0.1%)

localize10.0ms (0.1%)

rewrite52.0ms (0.5%)

series97.0ms (0.9%)

simplify44.0ms (0.4%)

prune35.0ms (0.3%)

localize9.0ms (0.1%)

rewrite150.0ms (1.4%)

series172.0ms (1.6%)

simplify100.0ms (0.9%)

prune109.0ms (1%)

localize33.0ms (0.3%)

rewrite890.0ms (8.4%)

series270.0ms (2.6%)

simplify106.0ms (1%)

prune727.0ms (6.9%)

localize54.0ms (0.5%)

rewrite1.3s (12.6%)

series324.0ms (3.1%)

simplify127.0ms (1.2%)

prune996.0ms (9.4%)

regimes429.0ms (4.1%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.4s (32.4%)

Profiling