Details

sample334.0ms

Algorithm

intervals

Results

44.0ms	208×	body	10240	exit
15.0ms	441×	body	80	nan
8.0ms	239×	body	80	valid
2.0ms	23×	body	160	valid

simplify78.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	7
1	28	7
2	41	7
3	75	7
4	182	7
5	576	7
6	2666	7
7	5001	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
0.2b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
4.6b	(- (exp (* 2.0 x)) 1.0)
4.7b	(- (exp x) 1.0)

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

92×	`add-sqr-sqrt`
89×	`*-un-lft-identity`
51×	`times-frac`
41×	`add-cube-cbrt`
31×	`sqrt-prod`
24×	`distribute-lft-out--` `difference-of-squares`
18×	`prod-diff`
8×	`add-log-exp`
6×	`add-exp-log` `fma-neg` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-/r` `flip--` `associate-/l`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u`
2×	`sub-neg` `rem-sqrt-square` `diff-log` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `div-exp` `clear-num`

Counts

4 → 155

Calls

4 calls:

9.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
10.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
5.0ms	(- (exp (* 2.0 x)) 1.0)
7.0ms	(- (exp x) 1.0)

series211.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
59.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
34.0ms	(- (exp (* 2.0 x)) 1.0)
23.0ms	(- (exp x) 1.0)

simplify60.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	480	1694
1	1523	1484
2	5001	1470

prune403.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (fma (- 1.0) 1.0 (exp (+ x x)))) (+ (exp x) 1.0)))
0.2b	(/ (- (exp (* 2.0 x)) 1.0) (fma (- 1.0) 1.0 (exp (+ x x))))
4.6b	(fma (- 1.0) 1.0 (exp (+ x x)))
4.6b	(- (exp (* 2.0 x)) 1.0)

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt` `*-un-lft-identity`
21×	`add-cube-cbrt`
15×	`times-frac`
9×	`prod-diff`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`sqrt-div` `associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-neg` `associate-/r*`
2×	`frac-times` `flip3--` `sqrt-pow1` `flip3-+` `associate-*r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `pow1/2` `diff-log` `div-sub` `div-exp` `pow-prod-down` `associate-*l/` `clear-num` `sqrt-prod` `fma-udef` `div-inv`

Counts

4 → 96

Calls

4 calls:

10.0ms	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (fma (- 1.0) 1.0 (exp (+ x x)))) (+ (exp x) 1.0)))
7.0ms	(/ (- (exp (* 2.0 x)) 1.0) (fma (- 1.0) 1.0 (exp (+ x x))))
1.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
5.0ms	(- (exp (* 2.0 x)) 1.0)

series440.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (fma (- 1.0) 1.0 (exp (+ x x)))) (+ (exp x) 1.0)))
203.0ms	(/ (- (exp (* 2.0 x)) 1.0) (fma (- 1.0) 1.0 (exp (+ x x))))
43.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
29.0ms	(- (exp (* 2.0 x)) 1.0)

simplify55.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	439	1178
1	1619	1042
2	5003	1028

prune362.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (fma (- 1.0) 1.0 (exp (+ x x)))) (+ (pow (exp x) 3) (pow 1.0 3)))) (sqrt (+ (* (exp x) (exp x)) (- (* 1.0 1.0) (* (exp x) 1.0)))))
4.6b	(- (exp (* 2.0 x)) 1.0)
4.6b	(fma (- 1.0) 1.0 (exp (+ x x)))
4.7b	(- (* 1.0 1.0) (* (exp x) 1.0))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt` `*-un-lft-identity`
28×	`add-cube-cbrt`
24×	`times-frac`
22×	`sqrt-prod`
10×	`prod-diff`
8×	`add-log-exp`
7×	`sqrt-div`
6×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
5×	`associate-/l/`
4×	`pow1` `expm1-log1p-u` `fma-neg` `log1p-expm1-u` `associate-/l*`
3×	`flip3-+` `flip-+`
2×	`frac-times` `sub-neg` `flip3--` `diff-log` `associate-*r/` `associate-/r/` `flip--`
1×	`cbrt-undiv` `sqrt-undiv` `distribute-rgt-out--` `frac-2neg` `div-exp` `associate-*l/` `clear-num` `fma-udef` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 111

Calls

4 calls:

31.0ms	(/ (sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (fma (- 1.0) 1.0 (exp (+ x x)))) (+ (pow (exp x) 3) (pow 1.0 3)))) (sqrt (+ (* (exp x) (exp x)) (- (* 1.0 1.0) (* (exp x) 1.0)))))
5.0ms	(- (exp (* 2.0 x)) 1.0)
1.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
4.0ms	(- (* 1.0 1.0) (* (exp x) 1.0))

series407.0ms

Counts

4 → 12

Calls

4 calls:

301.0ms	(/ (sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (fma (- 1.0) 1.0 (exp (+ x x)))) (+ (pow (exp x) 3) (pow 1.0 3)))) (sqrt (+ (* (exp x) (exp x)) (- (* 1.0 1.0) (* (exp x) 1.0)))))
26.0ms	(- (exp (* 2.0 x)) 1.0)
47.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
32.0ms	(- (* 1.0 1.0) (* (exp x) 1.0))

simplify83.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	565	2485
1	2160	2275
2	5001	2257

prune580.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

localize25.0ms

Local error

Found 4 expressions with local error:

4.6b	(fma (- 1.0) 1.0 (exp (+ x x)))
4.6b	(fma (- 1.0) 1.0 (exp (+ x x)))
4.6b	(- (exp (* 2.0 x)) 1.0)
4.6b	(- (exp (* 2.0 x)) 1.0)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
18×	`add-cube-cbrt` `prod-diff`
8×	`add-log-exp`
6×	`fma-neg`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
2×	`sub-neg` `flip3--` `diff-log` `flip--` `fma-udef` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 76

Calls

4 calls:

1.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
1.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
5.0ms	(- (exp (* 2.0 x)) 1.0)
5.0ms	(- (exp (* 2.0 x)) 1.0)

series143.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
48.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
26.0ms	(- (exp (* 2.0 x)) 1.0)
26.0ms	(- (exp (* 2.0 x)) 1.0)

simplify93.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 3 (81.0ms)

Iter	Nodes	Cost
0	182	644
1	540	464
2	2717	442
3	5001	370

prune349.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.2b

regimes36.0ms

Accuracy

73.1% (0.7b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 2.7b

bsearch33.0ms

Steps

Iters	Range		Point
5	-2.6173080331279203e-12	-1.0159879302621945e-12	-1.673419611240543e-12

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	26
1	36	26

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.4s	6824×	body	10240	exit
429.0ms	12951×	body	80	nan
254.0ms	7440×	body	80	valid
55.0ms	685×	body	160	valid