Details

analyze219.0ms (4.8%)

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)

sample56.0ms (1.2%)

Algorithm

1×

intervals

Results

20.0ms	68×	body	1024	valid
9.0ms	133×	body	128	valid
7.0ms	33×	body	512	valid
5.0ms	256×	pre	128	true
3.0ms	22×	body	256	valid

Compiler

Compiled 26 to 23 computations (11.5% saved)

simplify111.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	24	17
1	24	17

prune5.0ms (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: 0.2b

Counts

2 → 1

Compiler

Compiled 22 to 18 computations (18.2% saved)

localize10.0ms (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 (sin.f64 v))
0.2b	(*.f64 e (cos.f64 v))

rewrite21.0ms (0.5%)

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

series173.0ms (3.8%)

Counts

3 → 9

Calls

3 calls:

101.0ms	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))
39.0ms	(*.f64 e (cos.f64 v))
33.0ms	(*.f64 e (sin.f64 v))

simplify83.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4947	920
1	4947	920

prune69.0ms (1.5%)

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 1189 to 476 computations (60% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (sin.f64 v) (+.f64 (*.f64 e (cos.f64 v)) 1))
0.2b	(.f64 e (/.f64 (sin.f64 v) (+.f64 (.f64 e (cos.f64 v)) 1)))
0.2b	(*.f64 e (cos.f64 v))

rewrite28.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 81

Calls

3 calls:

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

series186.0ms (4.1%)

Counts

3 → 9

Calls

3 calls:

91.0ms	(.f64 e (/.f64 (sin.f64 v) (+.f64 (.f64 e (cos.f64 v)) 1)))
64.0ms	(/.f64 (sin.f64 v) (+.f64 (*.f64 e (cos.f64 v)) 1))
31.0ms	(*.f64 e (cos.f64 v))

simplify97.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	5416	1715

prune83.0ms (1.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	89	1	90
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	89	8	97

Merged error: 0.0b

Counts

97 → 8

Compiler

Compiled 1810 to 790 computations (56.4% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

rewrite28.0ms (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 (*.f64 e (cos.f64 v)) 1) (sin.f64 v)))
6.0ms	(/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) (sin.f64 v))
4.0ms	(*.f64 e (cos.f64 v))

series190.0ms (4.1%)

Counts

3 → 9

Calls

3 calls:

95.0ms	(/.f64 e (/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) (sin.f64 v)))
68.0ms	(/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) (sin.f64 v))
27.0ms	(*.f64 e (cos.f64 v))

simplify104.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4941	3222
1	4941	3222

prune125.0ms (2.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	121	5	126
Fresh	4	2	6
Picked	0	1	1
Done	0	1	1
Total	125	9	134

Merged error: 0b

Counts

134 → 9

Compiler

Compiled 2769 to 1149 computations (58.5% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite41.0ms (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 (.f64 e (cos.f64 v)) 1) (.f64 (sin.f64 v) (sqrt.f64 e))))
9.0ms	(/.f64 (+.f64 (.f64 e (cos.f64 v)) 1) (.f64 (sin.f64 v) (sqrt.f64 e)))
5.0ms	(*.f64 (sin.f64 v) (sqrt.f64 e))
4.0ms	(*.f64 e (cos.f64 v))

series310.0ms (6.8%)

Counts

4 → 12

Calls

4 calls:

128.0ms	(/.f64 (sqrt.f64 e) (/.f64 (+.f64 (.f64 e (cos.f64 v)) 1) (.f64 (sin.f64 v) (sqrt.f64 e))))
105.0ms	(/.f64 (+.f64 (.f64 e (cos.f64 v)) 1) (.f64 (sin.f64 v) (sqrt.f64 e)))
49.0ms	(*.f64 (sin.f64 v) (sqrt.f64 e))
27.0ms	(*.f64 e (cos.f64 v))

simplify85.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4981	3907
1	4981	3907

prune139.0ms (3%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	145	2	147
Fresh	3	3	6
Picked	0	1	1
Done	0	2	2
Total	148	8	156

Merged error: 0b

Counts

156 → 8

Compiler

Compiled 3400 to 1224 computations (64% saved)

regimes180.0ms (3.9%)

Compiler: Compiled 1820 to 1259 computations (30.8% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	17
1	14	17

end0.0ms (0%)

sample2.2s (48.2%)

Algorithm

1×

intervals

Results

623.0ms	2010×	body	1024	valid
324.0ms	4467×	body	128	valid
219.0ms	1013×	body	512	valid
160.0ms	8000×	pre	128	true
77.0ms	506×	body	256	valid
2.0ms	4×	body	2048	valid

Compiler

Compiled 624 to 434 computations (30.4% saved)

Details

analyze219.0ms (4.8%)

sample56.0ms (1.2%)

simplify111.0ms (2.4%)

prune5.0ms (0.1%)

localize10.0ms (0.2%)

rewrite21.0ms (0.5%)

series173.0ms (3.8%)

simplify83.0ms (1.8%)

prune69.0ms (1.5%)

localize9.0ms (0.2%)

rewrite28.0ms (0.6%)

series186.0ms (4.1%)

simplify97.0ms (2.1%)

prune83.0ms (1.8%)

localize9.0ms (0.2%)

rewrite28.0ms (0.6%)

series190.0ms (4.1%)

simplify104.0ms (2.3%)

prune125.0ms (2.7%)

localize11.0ms (0.2%)

rewrite41.0ms (0.9%)

series310.0ms (6.8%)

simplify85.0ms (1.8%)

prune139.0ms (3%)

regimes180.0ms (3.9%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample2.2s (48.2%)

Profiling