Details

sample118.0ms

Algorithm

intervals

Results

53.0ms	349×	body	80	valid
42.0ms	333×	body	80	nan

simplify65.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (22.0ms)

Iter	Nodes	Cost
0	40	12
1	92	12
2	269	12
3	669	12
4	1565	11
5	2855	11
6	5001	11

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 4.9b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
0.1b	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
0.2b	(* (- x 0.5) (log x))
4.5b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 114

Calls

4 calls:

34.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
19.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
11.0ms	(* (- x 0.5) (log x))
21.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series824.0ms

Counts

4 → 12

Calls

4 calls:

446.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
39.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
253.0ms	(* (- x 0.5) (log x))
86.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify74.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	606	918
1	2410	804
2	5001	787

prune465.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.2b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (- x 0.5) (log x) (- (* (sqrt x) (sqrt x))))
0.5b	(* (sqrt x) (sqrt x))
2.3b	(+ (+ 0.91893853320467 (- x)) x)
4.5b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt` `*-un-lft-identity`
21×	`add-cube-cbrt`
19×	`pow1`
18×	`sqrt-prod`
12×	`add-log-exp`
9×	`times-frac`
8×	`add-exp-log` `sqrt-pow1` `pow1/2` `swap-sqr` `add-cbrt-cube`
7×	`distribute-lft-out`
6×	`associate-r` `associate-l`
5×	`fma-def` `sum-log` `pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `unswap-sqr`
3×	`associate-+l-` `pow-prod-down` `associate-/r` `pow-sqr` `associate-/l`
2×	`distribute-rgt-neg-in` `flip3-+` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `pow2` `neg-sub0` `associate-+r-` `associate-+l+` `frac-2neg` `pow-plus` `sqrt-unprod` `div-exp` `unsub-neg` `neg-log` `prod-exp` `clear-num` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `fma-udef` `div-inv`

Counts

4 → 119

Calls

4 calls:

0.0ms	(fma (- x 0.5) (log x) (- (* (sqrt x) (sqrt x))))
7.0ms	(* (sqrt x) (sqrt x))
35.0ms	(+ (+ 0.91893853320467 (- x)) x)
21.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series299.0ms

Counts

4 → 12

Calls

4 calls:

197.0ms	(fma (- x 0.5) (log x) (- (* (sqrt x) (sqrt x))))
15.0ms	(* (sqrt x) (sqrt x))
1.0ms	(+ (+ 0.91893853320467 (- x)) x)
86.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify76.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	476	684
1	2396	578
2	5001	566

prune470.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 4.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (- x 0.5) (log x) (- (exp (log x))))
2.3b	(+ (+ 0.91893853320467 (- x)) x)
4.5b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)
5.9b	(exp (log x))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

27×	`*-un-lft-identity`
15×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`add-log-exp`
9×	`times-frac`
7×	`distribute-lft-out`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `fma-def` `sum-log`
4×	`expm1-log1p-u` `exp-prod` `log1p-expm1-u`
3×	`associate-+l-` `log-prod` `exp-sum` `associate-/r` `associate-/l`
2×	`distribute-rgt-neg-in` `flip3-+` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `neg-sub0` `associate-+r-` `associate-+l+` `frac-2neg` `div-exp` `unsub-neg` `neg-log` `clear-num` `log-pow` `fma-udef` `div-inv` `rem-exp-log`

Counts

4 → 85

Calls

4 calls:

0.0ms	(fma (- x 0.5) (log x) (- (exp (log x))))
36.0ms	(+ (+ 0.91893853320467 (- x)) x)
21.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)
2.0ms	(exp (log x))

series385.0ms

Counts

4 → 12

Calls

4 calls:

289.0ms	(fma (- x 0.5) (log x) (- (exp (log x))))
1.0ms	(+ (+ 0.91893853320467 (- x)) x)
85.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)
9.0ms	(exp (log x))

simplify40.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	392	588
1	1363	507
2	5001	492

prune394.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 4.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
0.1b	(fma (- x 0.5) (log x) (- (exp (log x))))
4.5b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)
5.9b	(exp (log x))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
4×	`expm1-log1p-u` `exp-prod` `log1p-expm1-u` `add-log-exp`
3×	`log-prod` `associate-r` `associate-l` `exp-sum` `associate-/r` `associate-/l`
2×	`associate-*l/` `associate-/l/`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `flip3-+` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `log-pow` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `fma-udef` `div-inv` `rem-exp-log` `unswap-sqr`

Counts

4 → 80

Calls

4 calls:

23.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
0.0ms	(fma (- x 0.5) (log x) (- (exp (log x))))
21.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)
2.0ms	(exp (log x))

series413.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
274.0ms	(fma (- x 0.5) (log x) (- (exp (log x))))
87.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)
9.0ms	(exp (log x))

simplify42.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	391	660
1	1324	582
2	5001	571

prune338.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 4.2b

regimes174.0ms

Accuracy

0% (1.4b remaining)

Error of 6.0b against oracle of 4.7b and baseline of 6.0b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	23
1	31	23

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.7s	11712×	body	80	valid
1.5s	11651×	body	80	nan