Details

analyze213.0ms (4.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	25%	75%	0
0%	25%	75%	1
12.5%	12.5%	75%	2
12.5%	12.5%	75%	3
18.7%	6.2%	75%	4
21.8%	3.1%	75%	5
23.4%	1.6%	75%	6
23.4%	1.6%	75%	7
24.2%	0.8%	75%	8
24.2%	0.8%	75%	9
24.6%	0.4%	75%	10
24.6%	0.4%	75%	11
24.8%	0.2%	75%	12
24.8%	0.2%	75%	13
24.9%	0.1%	75%	14

Compiler

Compiled 15 to 12 computations (20% saved)

sample57.0ms (1.1%)

Algorithm

1×

intervals

Results

21.0ms	56×	body	1024	valid
10.0ms	148×	body	128	valid
8.0ms	36×	body	512	valid
5.0ms	256×	pre	128	true
2.0ms	16×	body	256	valid

Compiler

Compiled 26 to 23 computations (11.5% saved)

simplify177.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	24	17
1	24	17

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: 0.1b

Counts

2 → 1

Compiler

Compiled 22 to 18 computations (18.2% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))
0.1b	(*.f64 e (cos.f64 v))
0.1b	(*.f64 e (sin.f64 v))

rewrite22.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64`
12×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
7×	`pow1_binary64`
6×	`associate-r_binary64` `associate-l_binary64`
3×	`associate-/r*_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `times-frac_binary64`
2×	`pow-prod-down_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `div-exp_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64` `flip-+_binary64`

Counts

3 → 59

Calls

3 calls:

6.0ms	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))
6.0ms	(*.f64 e (sin.f64 v))
4.0ms	(*.f64 e (cos.f64 v))

series309.0ms (6.1%)

Counts

3 → 9

Calls

3 calls:

167.0ms	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))
72.0ms	(*.f64 e (sin.f64 v))
69.0ms	(*.f64 e (cos.f64 v))

simplify58.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5009	920

prune73.0ms (1.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	61	7	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	7	69

Merged error: 0.0b

Counts

69 → 7

Compiler

Compiled 1178 to 473 computations (59.8% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.1b	(*.f64 e (cos.f64 v))
0.1b	(/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v))
0.2b	(/.f64 e (/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v)))

rewrite30.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`times-frac_binary64`
57×	`add-sqr-sqrt_binary64`
55×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
16×	`associate-/r*_binary64`
12×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`associate-/l*_binary64` `div-inv_binary64`
5×	`pow1_binary64`
4×	`cbrt-undiv_binary64` `div-exp_binary64`
3×	`add-log-exp_binary64` `associate-r_binary64` `associate-l_binary64`
2×	`associate-/l/_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `cbrt-unprod_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `flip-+_binary64` `*-commutative_binary64`

Counts

3 → 117

Calls

3 calls:

8.0ms	(/.f64 e (/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v)))
6.0ms	(/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v))
4.0ms	(*.f64 e (cos.f64 v))

series360.0ms (7.1%)

Counts

3 → 9

Calls

3 calls:

172.0ms	(/.f64 e (/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v)))
134.0ms	(/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v))
53.0ms	(*.f64 e (cos.f64 v))

simplify83.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4964	3208
1	4964	3208

prune120.0ms (2.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	124	2	126
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	126	7	133

Merged error: 0.0b

Counts

133 → 7

Compiler

Compiled 2694 to 1110 computations (58.8% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 e (cos.f64 v))
0.2b	(/.f64 (+.f64 1 (.f64 e (cos.f64 v))) (.f64 (sin.f64 v) (sqrt.f64 e)))
0.2b	(/.f64 (sqrt.f64 e) (/.f64 (+.f64 1 (.f64 e (cos.f64 v))) (.f64 (sin.f64 v) (sqrt.f64 e))))
0.3b	(*.f64 (sin.f64 v) (sqrt.f64 e))

rewrite43.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`times-frac_binary64`
47×	`add-sqr-sqrt_binary64`
41×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
28×	`sqrt-prod_binary64`
22×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`associate-r_binary64` `associate-/l*_binary64` `div-inv_binary64`
8×	`associate-/r*_binary64` `pow1_binary64`
7×	`cbrt-undiv_binary64` `div-exp_binary64`
6×	`associate-l_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
3×	`unswap-sqr_binary64`
2×	`pow-prod-down_binary64` `associate-/l/_binary64` `clear-num_binary64` `frac-2neg_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `associate-/r/_binary64` `flip-+_binary64`

Counts

4 → 135

Calls

4 calls:

11.0ms	(/.f64 (sqrt.f64 e) (/.f64 (+.f64 1 (.f64 e (cos.f64 v))) (.f64 (sin.f64 v) (sqrt.f64 e))))
8.0ms	(/.f64 (+.f64 1 (.f64 e (cos.f64 v))) (.f64 (sin.f64 v) (sqrt.f64 e)))
6.0ms	(*.f64 (sin.f64 v) (sqrt.f64 e))
4.0ms	(*.f64 e (cos.f64 v))

series566.0ms (11.1%)

Counts

4 → 12

Calls

4 calls:

210.0ms	(/.f64 (sqrt.f64 e) (/.f64 (+.f64 1 (.f64 e (cos.f64 v))) (.f64 (sin.f64 v) (sqrt.f64 e))))
205.0ms	(/.f64 (+.f64 1 (.f64 e (cos.f64 v))) (.f64 (sin.f64 v) (sqrt.f64 e)))
93.0ms	(*.f64 (sin.f64 v) (sqrt.f64 e))
57.0ms	(*.f64 e (cos.f64 v))

simplify109.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4940	3913
1	4940	3913

prune149.0ms (2.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	143	4	147
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	146	8	154

Merged error: 0b

Counts

154 → 8

Compiler

Compiled 3535 to 1310 computations (62.9% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 e (cos.f64 v))
0.2b	(/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sqrt.f64 e))
0.3b	(/.f64 (.f64 (sin.f64 v) (sqrt.f64 e)) (/.f64 (+.f64 1 (.f64 e (cos.f64 v))) (sqrt.f64 e)))
0.3b	(*.f64 (sin.f64 v) (sqrt.f64 e))

rewrite44.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`times-frac_binary64`
56×	`add-sqr-sqrt_binary64`
50×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
34×	`sqrt-prod_binary64`
28×	`associate-/r*_binary64`
22×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`associate-r_binary64`
8×	`pow1_binary64`
7×	`cbrt-undiv_binary64` `div-exp_binary64`
6×	`associate-l_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `associate-/l*_binary64` `div-inv_binary64`
3×	`unswap-sqr_binary64`
2×	`pow-prod-down_binary64` `associate-/l/_binary64` `clear-num_binary64` `frac-2neg_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `associate-/r/_binary64` `flip-+_binary64`

Counts

4 → 145

Calls

4 calls:

12.0ms	(/.f64 (.f64 (sin.f64 v) (sqrt.f64 e)) (/.f64 (+.f64 1 (.f64 e (cos.f64 v))) (sqrt.f64 e)))
6.0ms	(/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sqrt.f64 e))
6.0ms	(*.f64 (sin.f64 v) (sqrt.f64 e))
4.0ms	(*.f64 e (cos.f64 v))

series439.0ms (8.6%)

Counts

4 → 12

Calls

4 calls:

200.0ms	(/.f64 (.f64 (sin.f64 v) (sqrt.f64 e)) (/.f64 (+.f64 1 (.f64 e (cos.f64 v))) (sqrt.f64 e)))
102.0ms	(/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sqrt.f64 e))
87.0ms	(*.f64 (sin.f64 v) (sqrt.f64 e))
50.0ms	(*.f64 e (cos.f64 v))

simplify80.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4984	3672
1	4984	3672

prune148.0ms (2.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	157	0	157
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	157	8	165

Merged error: 0b

Counts

165 → 8

Compiler

Compiled 3588 to 1317 computations (63.3% saved)

regimes40.0ms (0.8%)

Compiler: Compiled 288 to 194 computations (32.6% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	17
1	13	17

end0.0ms (0%)

sample1.9s (37.7%)

Algorithm

1×

intervals

Results

755.0ms	2021×	body	1024	valid
313.0ms	4496×	body	128	valid
219.0ms	979×	body	512	valid
165.0ms	8000×	pre	128	true
77.0ms	495×	body	256	valid
8.0ms	9×	body	2048	valid

Compiler

Compiled 168 to 116 computations (31% saved)

Details

analyze213.0ms (4.2%)

sample57.0ms (1.1%)

simplify177.0ms (3.5%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

rewrite22.0ms (0.4%)

series309.0ms (6.1%)

simplify58.0ms (1.1%)

prune73.0ms (1.4%)

localize9.0ms (0.2%)

rewrite30.0ms (0.6%)

series360.0ms (7.1%)

simplify83.0ms (1.6%)

prune120.0ms (2.4%)

localize11.0ms (0.2%)

rewrite43.0ms (0.9%)

series566.0ms (11.1%)

simplify109.0ms (2.1%)

prune149.0ms (2.9%)

localize11.0ms (0.2%)

rewrite44.0ms (0.9%)

series439.0ms (8.6%)

simplify80.0ms (1.6%)

prune148.0ms (2.9%)

regimes40.0ms (0.8%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.9s (37.7%)

Profiling