Details

sample178.0ms

Algorithm

intervals

Results

76.0ms	1494×	body	80	nan
28.0ms	472×	body	80	valid

simplify49.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (4.0ms)

Iter	Nodes	Cost
0	32	10
1	65	10
2	181	8
3	522	8
4	2203	8
5	5002	8

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- t 1.0) (log a))
0.2b	(* y (log z))
1.0b	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
1.7b	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
15×	`add-cube-cbrt`
13×	`add-cbrt-cube`
12×	`add-exp-log` `log-prod`
10×	`pow1` `add-log-exp`
8×	`associate-r` `associate-l`
6×	`distribute-rgt-in` `distribute-lft-in`
5×	`exp-prod`
3×	`times-frac` `exp-sum` `prod-exp` `associate-/r*` `cbrt-unprod` `rem-exp-log`
2×	`cbrt-undiv` `exp-diff` `diff-log` `div-exp` `pow-prod-down` `associate-l/` `log-pow` `-commutative` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
1×	`sub-neg` `flip3--` `frac-2neg` `associate-r/` `associate--l+` `clear-num` `sum-log` `flip--` `div-inv` `associate-/l/` `associate-/l`

Counts

4 → 95

Calls

4 calls:

13.0ms	(* (- t 1.0) (log a))
4.0ms	(* y (log z))
32.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
80.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

series388.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* (- t 1.0) (log a))
36.0ms	(* y (log z))
119.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
176.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

simplify51.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	493	869
1	2033	715
2	5001	683

prune372.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))))
0.2b	(* y (log (/ 1 z)))
0.3b	(* (log (/ 1 a)) t)
1.7b	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))) y)

rewrite269.0ms

Algorithm

rewrite-expression-head

Rules

132×	`times-frac`
96×	`add-sqr-sqrt`
81×	`associate-r`
76×	`*-un-lft-identity`
75×	`add-cube-cbrt`
55×	`unpow-prod-down`
45×	`add-exp-log`
26×	`log-prod`
24×	`div-exp`
22×	`add-cbrt-cube`
17×	`exp-sum`
16×	`prod-exp`
14×	`pow1`
13×	`distribute-rgt-in` `distribute-lft-in`
12×	`associate-l`
8×	`pow-exp` `div-inv` `unswap-sqr`
6×	`log-pow` `cbrt-unprod`
5×	`cbrt-undiv` `sqr-pow`
4×	`add-log-exp`
3×	`pow-prod-down` `associate-/r` `-commutative`
2×	`pow-to-exp` `rec-exp` `pow-flip` `1-exp` `associate-*r/` `log-rec` `inv-pow`
1×	`distribute-lft-neg-out` `frac-2neg` `clear-num` `distribute-rgt-neg-out` `associate-/l/` `associate-/l*`

Counts

4 → 199

Calls

4 calls:

148.0ms	(* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))))
8.0ms	(* y (log (/ 1 z)))
5.0ms	(* (log (/ 1 a)) t)
98.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))) y)

series810.0ms

Counts

4 → 12

Calls

4 calls:

366.0ms	(* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))))
43.0ms	(* y (log (/ 1 z)))
61.0ms	(* (log (/ 1 a)) t)
340.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))) y)

simplify52.0ms

Algorithm

egg-herbie

Counts

211 → 211

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	1077	2667
1	5002	2322

prune808.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (/ 1 a)) t)
0.8b	(/ (* (sqrt (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))))) (sqrt (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))))) y)
2.8b	(sqrt (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))))
2.8b	(sqrt (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))))

rewrite856.0ms

Algorithm

rewrite-expression-head

Rules

14×	`pow1`
11×	`add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`associate-*r/`
6×	`sqrt-div` `associate-l`
4×	`sqrt-pow1` `add-log-exp`
3×	`times-frac` `associate-r` `pow-prod-down` `associate-/r*` `log-pow` `associate-/l/`
2×	`cbrt-undiv` `pow1/2` `div-exp` `prod-exp` `sqrt-prod` `cbrt-unprod`
1×	`distribute-lft-neg-out` `frac-times` `pow-flip` `frac-2neg` `log-rec` `associate-l/` `clear-num` `-commutative` `div-inv` `associate-/l*` `inv-pow` `unswap-sqr`

Counts

4 → 70

Calls

4 calls:

5.0ms	(* (log (/ 1 a)) t)
658.0ms	(/ (* (sqrt (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))))) (sqrt (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))))) y)
95.0ms	(sqrt (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))))
96.0ms	(sqrt (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))))

series1.6s

Counts

4 → 12

Calls

4 calls:

65.0ms	(* (log (/ 1 a)) t)
553.0ms	(/ (* (sqrt (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))))) (sqrt (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))))) y)
489.0ms	(sqrt (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))))
494.0ms	(sqrt (* x (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))))

simplify55.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	445	1344
1	1730	1084
2	5001	1051

prune447.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))
0.2b	(* y (log (/ 1 z)))
0.3b	(* (log (/ 1 a)) t)
6.2b	(/ (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))) (/ y x))

rewrite255.0ms

Algorithm

rewrite-expression-head

Rules

3085×	`times-frac`
1251×	`add-sqr-sqrt`
1247×	`add-cube-cbrt` `*-un-lft-identity`
728×	`unpow-prod-down`
238×	`exp-sum`
148×	`div-inv`
72×	`associate-/l*`
56×	`sqr-pow`
52×	`log-prod`
43×	`add-exp-log`
37×	`div-exp`
26×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in`
20×	`add-cbrt-cube`
13×	`associate-/r*`
12×	`pow1`
9×	`associate-r` `associate-l` `add-log-exp`
8×	`cbrt-undiv` `pow-exp`
6×	`log-pow`
3×	`sum-log`
2×	`pow-to-exp` `rec-exp` `pow-flip` `1-exp` `log-rec` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `inv-pow` `unswap-sqr`
1×	`+-commutative` `distribute-lft-neg-out` `associate-+r+` `frac-2neg` `flip3-+` `clear-num` `associate-/r/` `distribute-rgt-neg-out` `flip-+` `associate-/l/`

Counts

4 → 1160

Calls

4 calls:

15.0ms	(+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))
8.0ms	(* y (log (/ 1 z)))
5.0ms	(* (log (/ 1 a)) t)
101.0ms	(/ (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))) (/ y x))

series742.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))
38.0ms	(* y (log (/ 1 z)))
65.0ms	(* (log (/ 1 a)) t)
557.0ms	(/ (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))) (/ y x))

simplify284.0ms

Algorithm

egg-herbie

Counts

1172 → 1172

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5001	32805

prune6.0s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes173.0ms

Accuracy

96.4% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 1.2b

bsearch51.0ms

Steps

Iters	Range		Point
4	3.6450932906735275e-20	5.3575181912349926e-20	4.126712793956439e-20

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	29
1	34	29

end0.0ms

sample5.4s

Algorithm

intervals

Results

2.3s	45923×	body	80	nan
936.0ms	15168×	body	80	valid