Details

analyze1.0s (11.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
1.8%	98%	0.2%	10
7.7%	92.1%	0.2%	11
10.4%	89.4%	0.2%	12
14.9%	84.9%	0.2%	13
16.2%	83.5%	0.3%	14

Compiler

Compiled 14 to 12 computations (14.3% saved)

sample28.0ms (0.3%)

Algorithm

1×

intervals

Results

9.0ms	218×	body	128	valid
2.0ms	41×	body	128	invalid
2.0ms	15×	body	512	valid
1.0ms	9×	body	1024	valid
1.0ms	13×	body	256	valid
0.0ms	1×	body	2048	valid

Compiler

Compiled 27 to 28 computations (-3.7% saved)

simplify99.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (92.0ms)

Iter	Nodes	Cost
0	4917	19
1	4917	19

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

Merged error: 25.8b

Counts

2 → 1

Compiler

Compiled 26 to 22 computations (15.4% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(*.f64 (-.f64 y x) (-.f64 z t))
3.1b	(+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))
19.6b	(/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))

rewrite44.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
13×	`flip3--_binary64` `flip--_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`add-cube-cbrt_binary64`
8×	`associate-/l/_binary64` `frac-times_binary64`
6×	`cancel-sign-sub-inv_binary64`
5×	`associate-/r_binary64` `add-log-exp_binary64` `pow1_binary64` `associate-r_binary64` `associate-l*_binary64` `times-frac_binary64`
4×	`associate-r/_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `associate-l/_binary64`
2×	`sub-neg_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `prod-exp_binary64` `div-exp_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `distribute-lft-out_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `div-inv_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

3 → 85

Calls

3 calls:

15.0ms	(/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))
12.0ms	(*.f64 (-.f64 y x) (-.f64 z t))
9.0ms	(+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

series985.0ms (10.9%)

Counts

3 → 9

Calls

3 calls:

528.0ms	(+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))
388.0ms	(/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))
69.0ms	(*.f64 (-.f64 y x) (-.f64 z t))

simplify63.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	6926	1705

prune427.0ms (4.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	82	12	94
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	12	95

Merged error: 5.7b

Counts

95 → 12

Compiler

Compiled 9267 to 5177 computations (44.1% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 z t) (-.f64 a t))
1.8b	(*.f64 (-.f64 y x) (/.f64 (-.f64 z t) (-.f64 a t)))
3.1b	(+.f64 x (*.f64 (-.f64 y x) (/.f64 (-.f64 z t) (-.f64 a t))))

rewrite50.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

78×	`add-sqr-sqrt_binary64`
73×	`*-un-lft-identity_binary64`
51×	`times-frac_binary64`
31×	`associate-r_binary64`
27×	`add-cube-cbrt_binary64`
23×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`associate-/r_binary64` `add-log-exp_binary64` `pow1_binary64` `flip3--_binary64` `associate-l_binary64` `associate-/l_binary64` `flip--_binary64`
4×	`associate-/r/_binary64`
2×	`associate-/l/_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-inv_binary64` `div-exp_binary64` `frac-times_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `associate-r/_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

3 → 119

Calls

3 calls:

22.0ms	(*.f64 (-.f64 y x) (/.f64 (-.f64 z t) (-.f64 a t)))
10.0ms	(/.f64 (-.f64 z t) (-.f64 a t))
7.0ms	(+.f64 x (*.f64 (-.f64 y x) (/.f64 (-.f64 z t) (-.f64 a t))))

series1.0s (11.1%)

Counts

3 → 9

Calls

3 calls:

533.0ms	(+.f64 x (*.f64 (-.f64 y x) (/.f64 (-.f64 z t) (-.f64 a t))))
389.0ms	(*.f64 (-.f64 y x) (/.f64 (-.f64 z t) (-.f64 a t)))
85.0ms	(/.f64 (-.f64 z t) (-.f64 a t))

simplify66.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5509	2426

prune384.0ms (4.2%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	121	7	128
Fresh	3	8	11
Picked	0	1	1
Done	0	0	0
Total	124	16	140

Merged error: 5.7b

Counts

140 → 16

Compiler

Compiled 9237 to 4175 computations (54.8% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 a t) (-.f64 z t))
1.8b	(/.f64 (-.f64 y x) (/.f64 (-.f64 a t) (-.f64 z t)))
3.1b	(+.f64 x (/.f64 (-.f64 y x) (/.f64 (-.f64 a t) (-.f64 z t))))

rewrite120.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

330×	`times-frac_binary64`
323×	`*-un-lft-identity_binary64`
321×	`add-sqr-sqrt_binary64`
113×	`add-cube-cbrt_binary64`
104×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
36×	`associate-/r*_binary64`
15×	`associate-/r/_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l*_binary64`
9×	`flip3--_binary64` `flip--_binary64`
8×	`div-inv_binary64`
5×	`add-log-exp_binary64`
4×	`associate-/l/_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
3×	`pow1_binary64` `div-sub_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64`
1×	`flip3-+_binary64` `associate-+r-_binary64` `distribute-lft-out_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

3 → 274

Calls

3 calls:

53.0ms	(+.f64 x (/.f64 (-.f64 y x) (/.f64 (-.f64 a t) (-.f64 z t))))
20.0ms	(/.f64 (-.f64 y x) (/.f64 (-.f64 a t) (-.f64 z t)))
10.0ms	(/.f64 (-.f64 a t) (-.f64 z t))

series1.2s (12.8%)

Counts

3 → 9

Calls

3 calls:

534.0ms	(+.f64 x (/.f64 (-.f64 y x) (/.f64 (-.f64 a t) (-.f64 z t))))
534.0ms	(/.f64 (-.f64 y x) (/.f64 (-.f64 a t) (-.f64 z t)))
96.0ms	(/.f64 (-.f64 a t) (-.f64 z t))

simplify136.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

283 → 283

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4984	8451
1	4984	8451

prune393.0ms (4.3%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	279	4	283
Fresh	4	10	14
Picked	1	0	1
Done	0	1	1
Total	284	15	299

Merged error: 5.6b

Counts

299 → 15

Compiler

Compiled 11150 to 3244 computations (70.9% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (-.f64 z t))
0.6b	(cbrt.f64 (-.f64 z t))
1.8b	(.f64 (-.f64 y x) (/.f64 (.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (/.f64 (-.f64 a t) (cbrt.f64 (-.f64 z t)))))
7.5b	(+.f64 x (.f64 (-.f64 y x) (/.f64 (.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (/.f64 (-.f64 a t) (cbrt.f64 (-.f64 z t))))))

rewrite74.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

91×	`times-frac_binary64`
69×	`add-sqr-sqrt_binary64`
59×	`*-un-lft-identity_binary64`
51×	`associate-r_binary64`
36×	`cbrt-prod_binary64`
27×	`add-cube-cbrt_binary64`
22×	`add-exp-log_binary64`
16×	`add-cbrt-cube_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
7×	`cbrt-unprod_binary64` `prod-exp_binary64`
6×	`cbrt-div_binary64` `add-log-exp_binary64` `pow1_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
5×	`flip3--_binary64` `associate-l_binary64` `flip--_binary64`
4×	`unswap-sqr_binary64`
3×	`associate-/r/_binary64`
2×	`pow1/3_binary64` `div-inv_binary64` `frac-times_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `associate-r/_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

4 → 125

Calls

4 calls:

41.0ms	(.f64 (-.f64 y x) (/.f64 (.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (/.f64 (-.f64 a t) (cbrt.f64 (-.f64 z t)))))
5.0ms	(+.f64 x (.f64 (-.f64 y x) (/.f64 (.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (/.f64 (-.f64 a t) (cbrt.f64 (-.f64 z t))))))
4.0ms	(cbrt.f64 (-.f64 z t))
4.0ms	(cbrt.f64 (-.f64 z t))

series1.4s (15.1%)

Counts

4 → 12

Calls

4 calls:

545.0ms	(+.f64 x (.f64 (-.f64 y x) (/.f64 (.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (/.f64 (-.f64 a t) (cbrt.f64 (-.f64 z t))))))
394.0ms	(.f64 (-.f64 y x) (/.f64 (.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (/.f64 (-.f64 a t) (cbrt.f64 (-.f64 z t)))))
215.0ms	(cbrt.f64 (-.f64 z t))
212.0ms	(cbrt.f64 (-.f64 z t))

simplify81.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5296	3087

prune155.0ms (1.7%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	136	1	137
Fresh	0	13	13
Picked	0	1	1
Done	0	1	1
Total	136	16	152

Merged error: 5.6b

Counts

152 → 16

Compiler

Compiled 4788 to 1177 computations (75.4% saved)

regimes182.0ms (2%)

Compiler: Compiled 2000 to 1155 computations (42.3% saved)

bsearch70.0ms (0.8%)

Steps

Iters	Range		Point
11	3.7751693755606653e-193	7.093698993359153e-169	3.4738748046373586e-182
9	-4.516515589422377e-186	-3.531358057869628e-192	-8.513758409172267e-188

Compiler

Compiled 1 to 5 computations (-400% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	81	69
1	81	69

end0.0ms (0%)

sample1.1s (12%)

Algorithm

1×

intervals

Results

280.0ms	6654×	body	128	valid
58.0ms	387×	body	1024	valid
54.0ms	510×	body	512	valid
51.0ms	1233×	body	128	invalid
28.0ms	388×	body	256	valid
11.0ms	61×	body	2048	valid

Compiler

Compiled 506 to 287 computations (43.3% saved)

Details

analyze1.0s (11.4%)

sample28.0ms (0.3%)

simplify99.0ms (1.1%)

prune7.0ms (0.1%)

localize9.0ms (0.1%)

rewrite44.0ms (0.5%)

series985.0ms (10.9%)

simplify63.0ms (0.7%)

prune427.0ms (4.7%)

localize9.0ms (0.1%)

rewrite50.0ms (0.6%)

series1.0s (11.1%)

simplify66.0ms (0.7%)

prune384.0ms (4.2%)

localize10.0ms (0.1%)

rewrite120.0ms (1.3%)

series1.2s (12.8%)

simplify136.0ms (1.5%)

prune393.0ms (4.3%)

localize13.0ms (0.1%)

rewrite74.0ms (0.8%)

series1.4s (15.1%)

simplify81.0ms (0.9%)

prune155.0ms (1.7%)

regimes182.0ms (2%)

bsearch70.0ms (0.8%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.1s (12%)

Profiling