Details

analyze1.4s (13.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
0%	100%	0%	4
0%	100%	0%	5
0%	100%	0%	6
0%	100%	0%	7
0%	100%	0%	8
0%	100%	0%	9
0%	100%	0%	10
0%	100%	0%	11
0%	100%	0%	12
0%	100%	0%	13
0.1%	99.9%	0%	14

Compiler

Compiled 10 to 7 computations (30% saved)

sample193.0ms (2%)

Algorithm

1×

intervals

Results

124.0ms	64×	body	2048	valid
36.0ms	89×	body	1024	valid
10.0ms	44×	body	512	valid
7.0ms	5×	body	4096	valid
5.0ms	33×	body	256	valid
2.0ms	21×	body	128	valid

Compiler

Compiled 19 to 14 computations (26.3% saved)

simplify234.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	990	14
1	990	14

prune4.0ms (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

Merged error: 32.2b

Counts

2 → 1

Compiler

Compiled 18 to 12 computations (33.3% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
2.0b	(-.f64 x (tan.f64 x))
2.0b	(-.f64 x (sin.f64 x))

rewrite26.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
15×	`add-cube-cbrt_binary64`
14×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
7×	`add-log-exp_binary64`
5×	`associate-/r_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l_binary64`
4×	`flip3--_binary64` `flip--_binary64`
3×	`pow1_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `associate-/r/_binary64`
1×	`cbrt-undiv_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

3 → 78

Calls

3 calls:

9.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
6.0ms	(-.f64 x (sin.f64 x))
4.0ms	(-.f64 x (tan.f64 x))

series277.0ms (2.8%)

Counts

3 → 9

Calls

3 calls:

110.0ms	(-.f64 x (tan.f64 x))
109.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
57.0ms	(-.f64 x (sin.f64 x))

simplify102.0ms (1%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4845	1797
1	4845	1797

prune74.0ms (0.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	84	3	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	3	88

Merged error: 0b

Counts

88 → 3

Compiler

Compiled 1551 to 319 computations (79.4% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.1b	(*.f64 27/2800 (pow.f64 x 4))
0.2b	(.f64 (.f64 x x) 9/40)
14.1b	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))

rewrite24.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-exp-log_binary64` `add-sqr-sqrt_binary64`
10×	`associate-r_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64` `pow1_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`prod-exp_binary64`
4×	`cbrt-unprod_binary64` `associate-l_binary64` `unswap-sqr_binary64` `unpow-prod-down_binary64`
3×	`pow-prod-down_binary64`
2×	`diff-log_binary64` `sqr-pow_binary64` `*-commutative_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `associate--r+_binary64` `flip3--_binary64` `flip--_binary64` `pow-exp_binary64` `sum-log_binary64`

Counts

3 → 57

Calls

3 calls:

8.0ms	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))
6.0ms	(.f64 (.f64 x x) 9/40)
6.0ms	(*.f64 27/2800 (pow.f64 x 4))

series153.0ms (1.6%)

Counts

3 → 9

Calls

3 calls:

56.0ms	(*.f64 27/2800 (pow.f64 x 4))
52.0ms	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))
45.0ms	(.f64 (.f64 x x) 9/40)

simplify40.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	4833	850
1	4833	850

prune69.0ms (0.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	66	3	69

Merged error: 0b

Counts

69 → 3

Compiler

Compiled 1187 to 853 computations (28.1% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
0.0b	(log.f64 (exp.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))))
2.0b	(-.f64 x (tan.f64 x))
2.0b	(-.f64 x (sin.f64 x))

rewrite42.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
50×	`times-frac_binary64`
32×	`log-pow_binary64`
31×	`exp-prod_binary64`
28×	`add-cube-cbrt_binary64`
24×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
8×	`add-log-exp_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`associate-/r_binary64` `pow1_binary64` `flip3--_binary64` `associate-/l_binary64` `flip--_binary64`
4×	`associate-/r/_binary64`
3×	`log-prod_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `div-sub_binary64` `div-inv_binary64`
1×	`cbrt-undiv_binary64` `rem-log-exp_binary64` `exp-diff_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64` `log-div_binary64`

Counts

4 → 122

Calls

4 calls:

13.0ms	(log.f64 (exp.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))))
9.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
4.0ms	(-.f64 x (sin.f64 x))
4.0ms	(-.f64 x (tan.f64 x))

series406.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

170.0ms	(log.f64 (exp.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))))
109.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
89.0ms	(-.f64 x (tan.f64 x))
37.0ms	(-.f64 x (sin.f64 x))

simplify81.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5617	2686

prune102.0ms (1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	134	3	137

Merged error: 0b

Counts

137 → 3

Compiler

Compiled 2648 to 536 computations (79.8% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.0b	(-.f64 x (tan.f64 x))
2.0b	(-.f64 x (sin.f64 x))
2.0b	(-.f64 x (sin.f64 x))
2.0b	(-.f64 x (sin.f64 x))

rewrite22.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `add-sqr-sqrt_binary64`
4×	`sub-neg_binary64` `pow1_binary64` `flip3--_binary64` `diff-log_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip--_binary64`

Counts

4 → 52

Calls

4 calls:

4.0ms	(-.f64 x (sin.f64 x))
4.0ms	(-.f64 x (sin.f64 x))
4.0ms	(-.f64 x (sin.f64 x))
4.0ms	(-.f64 x (tan.f64 x))

series212.0ms (2.2%)

Counts

4 → 12

Calls

4 calls:

94.0ms	(-.f64 x (tan.f64 x))
40.0ms	(-.f64 x (sin.f64 x))
39.0ms	(-.f64 x (sin.f64 x))
39.0ms	(-.f64 x (sin.f64 x))

simplify76.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5011	778

prune69.0ms (0.7%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	64	3	67

Merged error: 0b

Counts

67 → 3

Compiler

Compiled 2390 to 329 computations (86.2% saved)

regimes45.0ms (0.5%)

Compiler: Compiled 193 to 99 computations (48.7% saved)

bsearch51.0ms (0.5%)

Steps

Iters	Range		Point
10	6.027278360775173e-08	21932.53696281882	0.026672942658527293
8	-0.4243026950196292	-8.724085136494892e-05	-0.0302404303590001

Compiler

Compiled 1 to 1 computations (0% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	91	101
1	91	101

end0.0ms (0%)

sample6.1s (62.4%)

Algorithm

1×

intervals

Results

4.0s	1987×	body	2048	valid
1.2s	2945×	body	1024	valid
322.0ms	1502×	body	512	valid
132.0ms	104×	body	4096	valid
116.0ms	770×	body	256	valid
59.0ms	692×	body	128	valid

Compiler

Compiled 130 to 63 computations (51.5% saved)

Details

analyze1.4s (13.7%)

sample193.0ms (2%)

simplify234.0ms (2.4%)

prune4.0ms (0%)

localize10.0ms (0.1%)

rewrite26.0ms (0.3%)

series277.0ms (2.8%)

simplify102.0ms (1%)

prune74.0ms (0.7%)

localize9.0ms (0.1%)

rewrite24.0ms (0.2%)

series153.0ms (1.6%)

simplify40.0ms (0.4%)

prune69.0ms (0.7%)

localize11.0ms (0.1%)

rewrite42.0ms (0.4%)

series406.0ms (4.1%)

simplify81.0ms (0.8%)

prune102.0ms (1%)

localize13.0ms (0.1%)

rewrite22.0ms (0.2%)

series212.0ms (2.2%)

simplify76.0ms (0.8%)

prune69.0ms (0.7%)

regimes45.0ms (0.5%)

bsearch51.0ms (0.5%)

simplify3.0ms (0%)

end0.0ms (0%)

sample6.1s (62.4%)

Profiling