Details

analyze221.0ms (3.8%)

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)

sample62.0ms (1.1%)

Algorithm

1×

intervals

Results

27.0ms	73×	body	1024	valid
9.0ms	137×	body	128	valid
8.0ms	35×	body	512	valid
5.0ms	256×	pre	128	true
2.0ms	11×	body	256	valid

Compiler

Compiled 26 to 23 computations (11.5% saved)

simplify179.0ms (3%)

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)

localize12.0ms (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))

rewrite23.0ms (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:

7.0ms	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))
7.0ms	(*.f64 e (sin.f64 v))
5.0ms	(*.f64 e (cos.f64 v))

series309.0ms (5.3%)

Counts

3 → 9

Calls

3 calls:

179.0ms	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))
71.0ms	(*.f64 e (sin.f64 v))
59.0ms	(*.f64 e (cos.f64 v))

simplify61.0ms (1%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5072	920

prune178.0ms (3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	59	9	68
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	59	10	69

Merged error: 0.0b

Counts

69 → 10

Compiler

Compiled 2864 to 1639 computations (42.8% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (log.f64 (exp.f64 (.f64 e (cos.f64 v))))))
0.1b	(*.f64 e (cos.f64 v))
0.1b	(*.f64 e (sin.f64 v))
6.9b	(log.f64 (exp.f64 (*.f64 e (cos.f64 v))))

rewrite26.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
11×	`pow1_binary64` `add-cube-cbrt_binary64`
6×	`associate-r_binary64` `associate-l_binary64`
5×	`associate-/r*_binary64` `add-log-exp_binary64` `log-pow_binary64` `times-frac_binary64`
4×	`distribute-lft-out_binary64`
3×	`cbrt-unprod_binary64` `log-prod_binary64` `prod-exp_binary64`
2×	`pow-prod-down_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `div-exp_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `rem-log-exp_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64` `exp-to-pow_binary64` `flip-+_binary64` `exp-prod_binary64`

Counts

4 → 77

Calls

4 calls:

8.0ms	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (log.f64 (exp.f64 (.f64 e (cos.f64 v))))))
5.0ms	(*.f64 e (sin.f64 v))
5.0ms	(*.f64 e (cos.f64 v))
2.0ms	(log.f64 (exp.f64 (*.f64 e (cos.f64 v))))

series423.0ms (7.2%)

Counts

4 → 12

Calls

4 calls:

227.0ms	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (log.f64 (exp.f64 (.f64 e (cos.f64 v))))))
83.0ms	(log.f64 (exp.f64 (*.f64 e (cos.f64 v))))
59.0ms	(*.f64 e (sin.f64 v))
54.0ms	(*.f64 e (cos.f64 v))

simplify72.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5127	1064

prune74.0ms (1.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	89	0	89
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	89	10	99

Merged error: 0.0b

Counts

99 → 10

Compiler

Compiled 1575 to 594 computations (62.3% saved)

localize10.0ms (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 (0.5%)

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))
5.0ms	(*.f64 e (cos.f64 v))

series348.0ms (5.9%)

Counts

3 → 9

Calls

3 calls:

166.0ms	(/.f64 e (/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v)))
130.0ms	(/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v))
51.0ms	(*.f64 e (cos.f64 v))

simplify100.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4938	3208
1	4938	3208

prune313.0ms (5.3%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	122	4	126
Fresh	5	2	7
Picked	0	1	1
Done	0	2	2
Total	127	9	136

Merged error: 0.0b

Counts

136 → 9

Compiler

Compiled 5821 to 3222 computations (44.6% saved)

localize12.0ms (0.2%)

Local error

Found 4 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 (sqrt.f64 e) (/.f64 (sqrt.f64 e) (/.f64 (+.f64 1 (.f64 e (cos.f64 v))) (sin.f64 v))))
0.3b	(/.f64 (sqrt.f64 e) (/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v)))

rewrite96.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 274

Calls

4 calls:

35.0ms	(.f64 (sqrt.f64 e) (/.f64 (sqrt.f64 e) (/.f64 (+.f64 1 (.f64 e (cos.f64 v))) (sin.f64 v))))
10.0ms	(/.f64 (sqrt.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))
6.0ms	(*.f64 e (cos.f64 v))

series682.0ms (11.6%)

Counts

4 → 12

Calls

4 calls:

294.0ms	(/.f64 (sqrt.f64 e) (/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v)))
214.0ms	(.f64 (sqrt.f64 e) (/.f64 (sqrt.f64 e) (/.f64 (+.f64 1 (.f64 e (cos.f64 v))) (sin.f64 v))))
124.0ms	(/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v))
50.0ms	(*.f64 e (cos.f64 v))

simplify134.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

286 → 286

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4962	8694
1	4962	8694

prune448.0ms (7.6%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	283	3	286
Fresh	2	3	5
Picked	0	1	1
Done	1	2	3
Total	286	9	295

Merged error: 0b

Counts

295 → 9

Compiler

Compiled 9539 to 4106 computations (57% saved)

regimes68.0ms (1.2%)

Compiler: Compiled 506 to 368 computations (27.3% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	17
1	14	17

end0.0ms (0%)

sample2.0s (33.5%)

Algorithm

1×

intervals

Results

751.0ms	2025×	body	1024	valid
325.0ms	4448×	body	128	valid
230.0ms	1015×	body	512	valid
153.0ms	8000×	pre	128	true
82.0ms	504×	body	256	valid
7.0ms	8×	body	2048	valid

Compiler

Compiled 186 to 137 computations (26.3% saved)

Details

analyze221.0ms (3.8%)

sample62.0ms (1.1%)

simplify179.0ms (3%)

prune4.0ms (0.1%)

localize12.0ms (0.2%)

rewrite23.0ms (0.4%)

series309.0ms (5.3%)

simplify61.0ms (1%)

prune178.0ms (3%)

localize12.0ms (0.2%)

rewrite26.0ms (0.4%)

series423.0ms (7.2%)

simplify72.0ms (1.2%)

prune74.0ms (1.3%)

localize10.0ms (0.2%)

rewrite30.0ms (0.5%)

series348.0ms (5.9%)

simplify100.0ms (1.7%)

prune313.0ms (5.3%)

localize12.0ms (0.2%)

rewrite96.0ms (1.6%)

series682.0ms (11.6%)

simplify134.0ms (2.3%)

prune448.0ms (7.6%)

regimes68.0ms (1.2%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.0s (33.5%)

Profiling