Details

sample153.0ms

Algorithm

intervals

Results

40.0ms	51×	body	10240	exit
32.0ms	43×	body	1280	valid
22.0ms	52×	body	640	valid
11.0ms	114×	body	80	valid
8.0ms	29×	body	320	valid
7.0ms	99×	body	80	nan
4.0ms	11×	body	640	nan
3.0ms	18×	body	160	valid
3.0ms	1×	body	2560	valid
2.0ms	7×	body	320	nan
1.0ms	2×	body	1280	nan
0.0ms	2×	body	160	nan

simplify220.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	20	7
1	35	7
2	53	7
3	81	7
4	121	7
5	250	7
6	314	7
7	532	7
8	908	7
9	1397	7
10	1553	7
11	1892	7
12	4682	7
13	5001	7

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.7b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* y (exp z))
0.0b	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
1.9b	(log (+ (- 1.0 y) (* y (exp z))))
3.6b	(+ (- 1.0 y) (* y (exp z)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
23×	`add-cube-cbrt`
12×	`times-frac`
11×	`pow1` `associate-+l+`
9×	`prod-diff` `add-log-exp`
8×	`add-exp-log` `add-cbrt-cube`
5×	`fma-def` `log-pow`
4×	`expm1-log1p-u` `log-div` `log1p-expm1-u` `associate-/l*`
3×	`log-prod` `flip3-+` `associate-r` `associate-l` `associate-/r*` `flip-+`
2×	`div-sub` `sum-log`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `sub-neg` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 102

Calls

4 calls:

5.0ms	(* y (exp z))
24.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
9.0ms	(log (+ (- 1.0 y) (* y (exp z))))
16.0ms	(+ (- 1.0 y) (* y (exp z)))

series70.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(* y (exp z))
43.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
15.0ms	(log (+ (- 1.0 y) (* y (exp z))))
7.0ms	(+ (- 1.0 y) (* y (exp z)))

simplify60.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	499	918
1	2002	785
2	5001	761

prune1.0s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 3.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (* y (exp z)))
0.6b	(cbrt (* y (exp z)))
2.4b	(log (+ (- 1.0 y) (* (* (cbrt (* y (exp z))) (cbrt (* y (exp z)))) (cbrt (* y (exp z))))))
13.9b	(+ (- 1.0 y) (* (* (cbrt (* y (exp z))) (cbrt (* y (exp z)))) (cbrt (* y (exp z)))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt` `*-un-lft-identity`
12×	`add-cube-cbrt`
11×	`associate-+l+`
9×	`prod-diff` `add-log-exp`
5×	`pow1` `add-exp-log` `fma-def`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`log-prod`
2×	`cbrt-prod` `log-div` `flip3-+` `pow1/3` `sum-log` `flip-+`
1×	`+-commutative` `associate-+l-` `sub-neg` `diff-log` `rem-log-exp` `log-pow` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 69

Calls

4 calls:

3.0ms	(cbrt (* y (exp z)))
3.0ms	(cbrt (* y (exp z)))
17.0ms	(log (+ (- 1.0 y) (* (* (cbrt (* y (exp z))) (cbrt (* y (exp z)))) (cbrt (* y (exp z))))))
20.0ms	(+ (- 1.0 y) (* (* (cbrt (* y (exp z))) (cbrt (* y (exp z)))) (cbrt (* y (exp z)))))

series56.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(cbrt (* y (exp z)))
14.0ms	(cbrt (* y (exp z)))
17.0ms	(log (+ (- 1.0 y) (* (* (cbrt (* y (exp z))) (cbrt (* y (exp z)))) (cbrt (* y (exp z))))))
11.0ms	(+ (- 1.0 y) (* (* (cbrt (* y (exp z))) (cbrt (* y (exp z)))) (cbrt (* y (exp z)))))

simplify44.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	349	1070
1	1313	765
2	5002	644

prune979.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 3.8b

localize22.0ms

Local error

Found 4 expressions with local error:

2.7b	(log (cbrt (+ (- 1.0 y) (* (* (cbrt (* y (exp z))) (cbrt (* y (exp z)))) (cbrt (* y (exp z)))))))
2.7b	(log (cbrt (+ (- 1.0 y) (* (* (cbrt (* y (exp z))) (cbrt (* y (exp z)))) (cbrt (* y (exp z)))))))
13.9b	(+ (- 1.0 y) (* (* (cbrt (* y (exp z))) (cbrt (* y (exp z)))) (cbrt (* y (exp z)))))
13.9b	(+ (- 1.0 y) (* (* (cbrt (* y (exp z))) (cbrt (* y (exp z)))) (cbrt (* y (exp z)))))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt` `*-un-lft-identity`
22×	`add-cube-cbrt` `associate-+l+`
18×	`prod-diff`
14×	`add-log-exp`
12×	`log-prod`
10×	`fma-def`
6×	`pow1` `add-exp-log` `cbrt-prod`
4×	`expm1-log1p-u` `log-div` `cbrt-div` `flip3-+` `sum-log` `log-pow` `add-cbrt-cube` `flip-+` `log1p-expm1-u`
2×	`+-commutative` `associate-+l-` `sub-neg` `pow1/3` `diff-log` `rem-log-exp` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 102

Calls

4 calls:

19.0ms	(log (cbrt (+ (- 1.0 y) (* (* (cbrt (* y (exp z))) (cbrt (* y (exp z)))) (cbrt (* y (exp z)))))))
17.0ms	(log (cbrt (+ (- 1.0 y) (* (* (cbrt (* y (exp z))) (cbrt (* y (exp z)))) (cbrt (* y (exp z)))))))
19.0ms	(+ (- 1.0 y) (* (* (cbrt (* y (exp z))) (cbrt (* y (exp z)))) (cbrt (* y (exp z)))))
20.0ms	(+ (- 1.0 y) (* (* (cbrt (* y (exp z))) (cbrt (* y (exp z)))) (cbrt (* y (exp z)))))

series96.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(log (cbrt (+ (- 1.0 y) (* (* (cbrt (* y (exp z))) (cbrt (* y (exp z)))) (cbrt (* y (exp z)))))))
38.0ms	(log (cbrt (+ (- 1.0 y) (* (* (cbrt (* y (exp z))) (cbrt (* y (exp z)))) (cbrt (* y (exp z)))))))
9.0ms	(+ (- 1.0 y) (* (* (cbrt (* y (exp z))) (cbrt (* y (exp z)))) (cbrt (* y (exp z)))))
9.0ms	(+ (- 1.0 y) (* (* (cbrt (* y (exp z))) (cbrt (* y (exp z)))) (cbrt (* y (exp z)))))

simplify47.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	329	2128
1	1163	1582
2	5002	1420

prune2.2s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 3.8b

localize15.0ms

Local error

Found 4 expressions with local error:

2.3b	(fma (/ (* z y) t) 1.0 (fma 0.5 (/ (* (pow z 2) y) t) (/ (log 1.0) t)))
4.3b	(/ (* z y) t)
7.4b	(/ (* (pow z 2) y) t)
8.5b	(* (pow z 2) y)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-exp-log`
17×	`add-sqr-sqrt`
16×	`add-cbrt-cube`
11×	`add-cube-cbrt` `*-un-lft-identity`
8×	`associate-l`
7×	`prod-exp`
6×	`times-frac` `div-exp` `associate-/r*`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `unpow-prod-down` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`associate-r` `cbrt-unprod`
2×	`pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `div-inv` `associate-/l*` `unpow2` `sqr-pow`
1×	`*-commutative` `fma-udef`

Counts

4 → 87

Calls

4 calls:

0.0ms	(fma (/ (* z y) t) 1.0 (fma 0.5 (/ (* (pow z 2) y) t) (/ (log 1.0) t)))
3.0ms	(/ (* z y) t)
4.0ms	(/ (* (pow z 2) y) t)
6.0ms	(* (pow z 2) y)

series37.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(fma (/ (* z y) t) 1.0 (fma 0.5 (/ (* (pow z 2) y) t) (/ (log 1.0) t)))
5.0ms	(/ (* z y) t)
6.0ms	(/ (* (pow z 2) y) t)
4.0ms	(* (pow z 2) y)

simplify46.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	300	473
1	1353	406
2	5002	406

prune771.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 3.4b

regimes1.1s

Accuracy

70.3% (5.2b remaining)

Error of 9.1b against oracle of 3.9b and baseline of 21.5b

bsearch94.0ms

Steps

Iters	Range		Point
5	4.2185849944799077e-221	9.771091612138487e-221	9.274120679861768e-221
7	-91.73841076085421	-0.49115008736797033	-0.4984438493979181

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	40
1	50	40

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.1s	1483×	body	10240	exit
1.0s	1451×	body	1280	valid
673.0ms	1536×	body	640	valid
343.0ms	3588×	body	80	valid
257.0ms	886×	body	320	valid
171.0ms	2409×	body	80	nan
100.0ms	66×	body	2560	valid
90.0ms	259×	body	640	nan
90.0ms	500×	body	160	valid
56.0ms	112×	body	1280	nan
46.0ms	196×	body	320	nan
19.0ms	113×	body	160	nan