Details

analyze2.0s (14%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5017	231
0	5	5
1	5	5

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
1.6%	98.2%	0.2%	10
3.1%	90.4%	6.5%	11
9.2%	84.4%	6.5%	12
13%	80.6%	6.5%	13
24.8%	68.7%	6.5%	14

Symmetry

(sort x y)

(sort t a)

Compiler

Compiled 15 to 13 computations (13.3% saved)

sample58.0ms (0.4%)

Algorithm

1×

intervals

Results

19.0ms	256×	body	128	valid
3.0ms	77×	body	128	nan
1.0ms	21×	body	128	invalid

Compiler

Compiled 29 to 30 computations (-3.4% saved)

simplify58.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	806	21
1	806	21

prune3.0ms (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

Error

20.0b

Counts

2 → 1

Compiler

Compiled 28 to 24 computations (14.3% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(-.f64 (.f64 z z) (.f64 t a))
4.2b	(.f64 (.f64 x y) z)
6.3b	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
22.2b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite132.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

17.1b

Rules

18×	`add-exp-log_binary64_9323` `add-cbrt-cube_binary64_9321`
11×	`add-sqr-sqrt_binary64_9307`
10×	`pow1_binary64_9346` `add-cube-cbrt_binary64_9320` `*-un-lft-identity_binary64_9285`
9×	`sqrt-prod_binary64_9301`
6×	`add-log-exp_binary64_9324` `prod-exp_binary64_9334` `cbrt-unprod_binary64_9318` `times-frac_binary64_9291` `associate-/r*_binary64_9229`
4×	`sqrt-div_binary64_9302`
3×	`flip3--_binary64_9289` `flip--_binary64_9260` `div-exp_binary64_9336` `cbrt-undiv_binary64_9319` `pow-prod-down_binary64_9356` `associate-r_binary64_9225`
2×	`associate-/r/_binary64_9231`
1×	`pow1/2_binary64_9365` `sqrt-pow1_binary64_9303` `rem-sqrt-square_binary64_9298` `frac-2neg_binary64_9296` `clear-num_binary64_9284` `div-inv_binary64_9282` `associate-/l_binary64_9230` `associate-l_binary64_9226` `-commutative_binary64_9216` `diff-log_binary64_9377` `sub-neg_binary64_9278` `cancel-sign-sub-inv_binary64_9251`

Counts

4 → 76

Calls

4 calls:

19.0ms	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
9.0ms	(.f64 (.f64 x y) z)
8.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
6.0ms	(-.f64 (.f64 z z) (.f64 t a))

Compiler

Compiled 1787 to 278 computations (84.4% saved)

series949.0ms (6.7%)

Error

3.6b

Counts

4 → 64

Calls

4 calls:

482.0ms	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
149.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
146.0ms	(-.f64 (.f64 z z) (.f64 t a))
114.0ms	(.f64 (.f64 x y) z)

Compiler

Compiled 2765 to 1944 computations (29.7% saved)

simplify76.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5467	2173

prune127.0ms (0.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	134	6	140
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	134	7	141

Error

3.6b

Counts

141 → 7

Compiler

Compiled 2460 to 437 computations (82.2% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
0.4b	(-.f64 (.f64 z z) (.f64 t a))
2.8b	(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
22.2b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite137.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

3.6b

Rules

36×	`times-frac_binary64_9291`
34×	`add-sqr-sqrt_binary64_9307`
33×	`add-cube-cbrt_binary64_9320` `*-un-lft-identity_binary64_9285`
24×	`sqrt-prod_binary64_9301` `associate-r_binary64_9225`
18×	`add-exp-log_binary64_9323` `add-cbrt-cube_binary64_9321`
10×	`pow1_binary64_9346`
6×	`add-log-exp_binary64_9324` `sqrt-div_binary64_9302` `prod-exp_binary64_9334` `cbrt-unprod_binary64_9318` `associate-/r*_binary64_9229`
4×	`flip3--_binary64_9289` `flip--_binary64_9260` `associate-/r/_binary64_9231`
3×	`pow-prod-down_binary64_9356` `div-exp_binary64_9336` `cbrt-undiv_binary64_9319` `associate-/l*_binary64_9230`
2×	`div-inv_binary64_9282`
1×	`pow1/2_binary64_9365` `sqrt-pow1_binary64_9303` `rem-sqrt-square_binary64_9298` `associate-r/_binary64_9227` `associate-l_binary64_9226` `-commutative_binary64_9216` `diff-log_binary64_9377` `sub-neg_binary64_9278` `cancel-sign-sub-inv_binary64_9251` `frac-2neg_binary64_9296` `clear-num_binary64_9284`

Counts

4 → 112

Calls

4 calls:

13.0ms	(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
7.0ms	(/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
4.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
4.0ms	(-.f64 (.f64 z z) (.f64 t a))

Compiler

Compiled 2928 to 440 computations (85% saved)

series978.0ms (6.9%)

Error

3.6b

Counts

4 → 68

Calls

4 calls:

485.0ms	(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
156.0ms	(/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
149.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
146.0ms	(-.f64 (.f64 z z) (.f64 t a))

Compiler

Compiled 2975 to 2221 computations (25.3% saved)

simplify71.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4974	3299
1	4974	3299

prune136.0ms (1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	180	0	180
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	180	7	187

Error

3.6b

Counts

187 → 7

Compiler

Compiled 3473 to 595 computations (82.9% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b	(/.f64 (.f64 x y) (fabs.f64 (cbrt.f64 (-.f64 (.f64 z z) (*.f64 t a)))))
5.9b	(.f64 (/.f64 (.f64 x y) (fabs.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 t a))))) (/.f64 z (sqrt.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
22.9b	(cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
22.9b	(cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite187.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

3.6b

Rules

40×	`add-sqr-sqrt_binary64_9307`
36×	`times-frac_binary64_9291`
33×	`associate-r_binary64_9225`
30×	`add-exp-log_binary64_9323` `add-cbrt-cube_binary64_9321`
29×	`add-cube-cbrt_binary64_9320` `*-un-lft-identity_binary64_9285`
20×	`sqrt-prod_binary64_9301`
16×	`cbrt-prod_binary64_9316`
9×	`div-exp_binary64_9336` `prod-exp_binary64_9334` `cbrt-unprod_binary64_9318` `cbrt-undiv_binary64_9319`
7×	`associate-l_binary64_9226`
6×	`pow1_binary64_9346` `cbrt-div_binary64_9317`
4×	`add-log-exp_binary64_9324` `unswap-sqr_binary64_9253`
3×	`flip3--_binary64_9289` `flip--_binary64_9260` `div-inv_binary64_9282` `associate-/r*_binary64_9229`
2×	`pow1/3_binary64_9367` `sqrt-div_binary64_9302` `associate-/r/_binary64_9231`
1×	`pow-prod-down_binary64_9356` `frac-times_binary64_9295` `associate-l/_binary64_9228` `associate-r/_binary64_9227` `-commutative_binary64_9216` `frac-2neg_binary64_9296` `clear-num_binary64_9284` `associate-/l_binary64_9230`

Counts

4 → 115

Calls

4 calls:

25.0ms	(.f64 (/.f64 (.f64 x y) (fabs.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 t a))))) (/.f64 z (sqrt.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
4.0ms	(/.f64 (.f64 x y) (fabs.f64 (cbrt.f64 (-.f64 (.f64 z z) (*.f64 t a)))))
4.0ms	(cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
4.0ms	(cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

Compiler

Compiled 4632 to 478 computations (89.7% saved)

series2.3s (16.3%)

Error

3.6b

Counts

4 → 64

Calls

4 calls:

1.0s	(.f64 (/.f64 (.f64 x y) (fabs.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 t a))))) (/.f64 z (sqrt.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
475.0ms	(cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
460.0ms	(/.f64 (.f64 x y) (fabs.f64 (cbrt.f64 (-.f64 (.f64 z z) (*.f64 t a)))))
240.0ms	(cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

Compiler

Compiled 6002 to 4165 computations (30.6% saved)

simplify129.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5051	5583

prune175.0ms (1.2%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	178	1	179
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	178	8	186

Error

3.6b

Counts

186 → 8

Compiler

Compiled 5844 to 821 computations (86% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.9b	(.f64 (/.f64 x 1) (.f64 (/.f64 z (sqrt.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 t a))))) (/.f64 y (fabs.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))))
6.6b	(.f64 (/.f64 z (sqrt.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 t a))))) (/.f64 y (fabs.f64 (cbrt.f64 (-.f64 (.f64 z z) (*.f64 t a))))))
22.9b	(cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
22.9b	(cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite292.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Error

3.6b

Rules

75×	`add-exp-log_binary64_9323`
65×	`add-sqr-sqrt_binary64_9307`
57×	`add-cbrt-cube_binary64_9321`
55×	`times-frac_binary64_9291`
46×	`associate-l_binary64_9226`
39×	`add-cube-cbrt_binary64_9320` `*-un-lft-identity_binary64_9285`
31×	`prod-exp_binary64_9334`
26×	`div-exp_binary64_9336`
22×	`cbrt-unprod_binary64_9318` `sqrt-prod_binary64_9301`
17×	`cbrt-prod_binary64_9316` `cbrt-undiv_binary64_9319`
14×	`associate-r_binary64_9225`
11×	`pow1_binary64_9346`
8×	`unswap-sqr_binary64_9253`
6×	`cbrt-div_binary64_9317` `frac-times_binary64_9295` `associate-*r/_binary64_9227`
5×	`1-exp_binary64_9329`
4×	`add-log-exp_binary64_9324` `pow-prod-down_binary64_9356` `associate-*l/_binary64_9228`
3×	`flip3--_binary64_9289` `flip--_binary64_9260` `div-inv_binary64_9282`
2×	`pow1/3_binary64_9367` `sqrt-div_binary64_9302` `associate-/r/_binary64_9231` `*-commutative_binary64_9216`

Counts

4 → 156

Calls

4 calls:

33.0ms	(.f64 (/.f64 x 1) (.f64 (/.f64 z (sqrt.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 t a))))) (/.f64 y (fabs.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))))
28.0ms	(.f64 (/.f64 z (sqrt.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 t a))))) (/.f64 y (fabs.f64 (cbrt.f64 (-.f64 (.f64 z z) (*.f64 t a))))))
4.0ms	(cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
4.0ms	(cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

Compiler

Compiled 6723 to 1099 computations (83.7% saved)

series2.3s (16.5%)

Error

3.6b

Counts

4 → 64

Calls

4 calls:

1.0s	(.f64 (/.f64 x 1) (.f64 (/.f64 z (sqrt.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 t a))))) (/.f64 y (fabs.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))))
684.0ms	(.f64 (/.f64 z (sqrt.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 t a))))) (/.f64 y (fabs.f64 (cbrt.f64 (-.f64 (.f64 z z) (*.f64 t a))))))
252.0ms	(cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
243.0ms	(cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

Compiler

Compiled 6652 to 4928 computations (25.9% saved)

simplify126.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

220 → 220

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5052	7837

prune254.0ms (1.8%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	220	0	220
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	220	8	228

Error

3.6b

Counts

228 → 8

Compiler

Compiled 7538 to 1407 computations (81.3% saved)

regimes1.2s (8.5%)

Accuracy

Total 3.2b remaining (49.4%)

Threshold costs 0b (0%)

Compiler

Compiled 9120 to 5977 computations (34.5% saved)

bsearch76.0ms (0.5%)

Steps

Iters	Range		Point
10	6.093844524704292e+85	1.1290235454833277e+101	1.602621992650537e+97
6	-2.886151319062817e+121	-4.7589209837107184e+120	-2.6800413878322386e+121

Compiler

Compiled 1 to 5 computations (-400% saved)

simplify25.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	71	43
1	71	43

Remove

(sort t a)

(sort x y)

Compiler

Compiled 116 to 76 computations (34.5% saved)

end0.0ms (0%)

sample2.3s (16.2%)

Algorithm

1×

intervals

Results

541.0ms	8000×	body	128	valid
127.0ms	2117×	body	128	nan
57.0ms	824×	body	128	invalid

Compiler

Compiled 1098 to 722 computations (34.2% saved)

Details

analyze2.0s (14%)

sample58.0ms (0.4%)

simplify58.0ms (0.4%)

prune3.0ms (0%)

localize21.0ms (0.1%)

rewrite132.0ms (0.9%)

series949.0ms (6.7%)

simplify76.0ms (0.5%)

prune127.0ms (0.9%)

localize10.0ms (0.1%)

rewrite137.0ms (1%)

series978.0ms (6.9%)

simplify71.0ms (0.5%)

prune136.0ms (1%)

localize18.0ms (0.1%)

rewrite187.0ms (1.3%)

series2.3s (16.3%)

simplify129.0ms (0.9%)

prune175.0ms (1.2%)

localize17.0ms (0.1%)

rewrite292.0ms (2.1%)

series2.3s (16.5%)

simplify126.0ms (0.9%)

prune254.0ms (1.8%)

regimes1.2s (8.5%)

bsearch76.0ms (0.5%)

simplify25.0ms (0.2%)

end0.0ms (0%)

sample2.3s (16.2%)

Profiling